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1. Binary refinement implies discrete exponentiation Aczel, Peteret al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt594",{id:"formSmash:items:resultList:0:j_idt594",widgetVar:"widget_formSmash_items_resultList_0_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Crosilla, LauraIshihara, HajimePalmgren, ErikUppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.Schuster, PeterPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Binary refinement implies discrete exponentiation2006In: Studia Logica, Vol. 84, p. 361-368Article in journal (Refereed)2. A zero-one law for <em>l</em>-colourable structures with a vectorspace pregeometry Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt591",{id:"formSmash:items:resultList:1:j_idt591",widgetVar:"widget_formSmash_items_resultList_1_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A zero-one law for*l*-colourable structures with a vectorspace pregeometry2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_1_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:1:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_1_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:1:j_idt854:0:fullText"});}); 3. Homogenizable structures and model completeness Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt591",{id:"formSmash:items:resultList:2:j_idt591",widgetVar:"widget_formSmash_items_resultList_2_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homogenizable structures and model completeness2016In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, no 7-8, p. 977-995Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:2:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_2_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:2:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_2_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:2:j_idt854:0:fullText"});}); 4. >k-homogeneous infinite graphs Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt591",{id:"formSmash:items:resultList:3:j_idt591",widgetVar:"widget_formSmash_items_resultList_3_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); >k-homogeneous infinite graphs2018In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, p. 160-174Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:3:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we give an explicit classification for the countably infinite graphs G which are, for some

*k*, ≥*k*-homogeneous. It turns out that a ≥*k*-homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_3_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:3:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_3_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:3:j_idt854:0:fullText"});}); 5. Limit Laws, Homogenizable Structures and Their Connections Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt591",{id:"formSmash:items:resultList:4:j_idt591",widgetVar:"widget_formSmash_items_resultList_4_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Limit Laws, Homogenizable Structures and Their Connections2018Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:4:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis is in the field of mathematical logic and especially model theory. The thesis contain six papers where the common theme is the Rado graph R. Some of the interesting abstract properties of R are that it is simple, homogeneous (and thus countably categorical), has SU-rank 1 and trivial dependence. The Rado graph is possible to generate in a probabilistic way. If we let K be the set of all finite graphs then we obtain R as the structure which satisfy all properties which hold with assymptotic probability 1 in K. On the other hand, since the Rado graph is homogeneous, it is also possible to generate it as a Fraïssé-limit of its age.

Paper I studies the binary structures which are simple, countably categorical, with SU-rank 1 and trivial algebraic closure. The main theorem shows that these structures are all possible to generate using a similar probabilistic method which is used to generate the Rado graph. Paper II looks at the simple homogeneous structures in general and give certain technical results on the subsets of SU-rank 1.

Paper III considers the set K consisting of all colourable structures with a definable pregeometry and shows that there is a 0-1 law and almost surely a unique definable colouring. When generating the Rado graph we almost surely have only rigid structures in K. Paper IV studies what happens if the structures in K are only the non-rigid finite structures. We deduce that the limit structures essentially try to stay as rigid as possible, given the restriction, and that we in general get a limit law but not a 0-1 law.

Paper V looks at the Rado graph's close cousin the random t-partite graph and notices that this structure is not homogeneous but almost homogeneous. Rather we may just add a definable binary predicate, which hold for any two elemenets which are in the same part, in order to make it homogeneous. This property is called being homogenizable and in Paper V we do a general study of homogenizable structures. Paper VI conducts a special case study of the homogenizable graphs which are the closest to being homogeneous, providing an explicit classification of these graphs.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); List of papers PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt633",{id:"formSmash:items:resultList:4:j_idt633",widgetVar:"widget_formSmash_items_resultList_4_j_idt633",onLabel:"List of papers",offLabel:"List of papers",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 1. Simple structures axiomatized by almost sure theoriesOpen this publication in new window or tab >>Simple structures axiomatized by almost sure theories### Ahlman, Ove

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_0_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:0:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_0_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_0_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:0:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_0_overlay_otherAuthors",multiple:true}); 2016 (English)In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, no 5, p. 435-456Article in journal (Refereed) Published##### Abstract [en]

In this article we give a classification of the binary, simple,

*ω*-categorical structures with*SU*-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as*ω*-stability or strong minimality.##### Keywords

Random structure, Almost sure theory, Pregeometry, Supersimple, Countably categorical##### National Category

Algebra and Logic##### Research subject

Mathematics##### Identifiers

urn:nbn:se:uu:diva-276995 (URN)10.1016/j.apal.2016.02.001 (DOI)000372680500001 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:0:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:0:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:0:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_0_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay908140",{id:"formSmash:items:resultList:4:j_idt634:0:j_idt638",widgetVar:"overlay908140",target:"formSmash:items:resultList:4:j_idt634:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 2. On sets with rank one in simple homogeneous structuresOpen this publication in new window or tab >>On sets with rank one in simple homogeneous structures### Ahlman, Ove

### Koponen, Vera

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_1_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:1:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_1_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_1_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:1:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_1_overlay_otherAuthors",multiple:true}); 2015 (English)In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, p. 223-250Article in journal (Refereed) Published##### Abstract [en]

We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

##### Keywords

model theory, homogeneous structure, simple theory, pregeometry, rank, reduct, random structure##### National Category

Algebra and Logic##### Research subject

Mathematics##### Identifiers

urn:nbn:se:uu:diva-243006 (URN)10.4064/fm228-3-2 (DOI)000352858400002 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:1:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:1:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:1:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_1_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay785724",{id:"formSmash:items:resultList:4:j_idt634:1:j_idt638",widgetVar:"overlay785724",target:"formSmash:items:resultList:4:j_idt634:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 3. Random l-colourable structures with a pregeometryOpen this publication in new window or tab >>Random l-colourable structures with a pregeometry### Ahlman, Ove

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.### Koponen, Vera

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_2_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:2:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_2_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_2_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:2:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_2_overlay_otherAuthors",multiple:true}); 2017 (English)In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, no 1-2, p. 32-58Article in journal (Refereed) Published##### Abstract [en]

We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

##### Place, publisher, year, edition, pages

Wiley-VCH Verlagsgesellschaft, 2017##### National Category

Algebra and Logic##### Research subject

Mathematical Logic##### Identifiers

urn:nbn:se:uu:diva-321515 (URN)10.1002/malq.201500006 (DOI)000400361900003 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:2:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:2:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:2:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_2_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay1093452",{id:"formSmash:items:resultList:4:j_idt634:2:j_idt638",widgetVar:"overlay1093452",target:"formSmash:items:resultList:4:j_idt634:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 4. Limit laws and automorphism groups of random nonrigid structuresOpen this publication in new window or tab >>Limit laws and automorphism groups of random nonrigid structures### Ahlman, Ove

### Koponen, Vera

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_3_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:3:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_3_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_3_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:3:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_3_overlay_otherAuthors",multiple:true}); 2015 (English)In: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, no 2, p. 1-53, article id 1Article in journal (Refereed) Published##### Abstract [en]

A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

##### Keywords

finite model theory, limit law, zero-one law, random structure, automorphism group##### National Category

Algebra and Logic##### Research subject

Mathematical Logic##### Identifiers

urn:nbn:se:uu:diva-248078 (URN)10.4115/jla.2015.7.2 (DOI)000359802400001 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:3:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:3:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:3:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_3_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay798508",{id:"formSmash:items:resultList:4:j_idt634:3:j_idt638",widgetVar:"overlay798508",target:"formSmash:items:resultList:4:j_idt634:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 5. Homogenizable structures and model completenessOpen this publication in new window or tab >>Homogenizable structures and model completeness### Ahlman, Ove

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_4_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:4:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_4_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_4_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:4:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_4_overlay_otherAuthors",multiple:true}); 2016 (English)In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, no 7-8, p. 977-995Article in journal (Refereed) Published##### Abstract [en]

A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

##### Keywords

Homogenizable, Model-complete, Amalgamation class, Quantifier-elimination##### National Category

Algebra and Logic##### Research subject

Mathematics##### Identifiers

urn:nbn:se:uu:diva-303714 (URN)10.1007/s00153-016-0507-6 (DOI)000385155700010 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:4:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:4:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:4:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_4_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay973821",{id:"formSmash:items:resultList:4:j_idt634:4:j_idt638",widgetVar:"overlay973821",target:"formSmash:items:resultList:4:j_idt634:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 6. >k-homogeneous infinite graphsOpen this publication in new window or tab >>>k-homogeneous infinite graphs### Ahlman, Ove

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_5_overlay_some",{id:"formSmash:items:resultList:4:j_idt634:5:overlay:some",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_5_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_5_overlay_otherAuthors",{id:"formSmash:items:resultList:4:j_idt634:5:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_5_overlay_otherAuthors",multiple:true}); 2018 (English)In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, p. 160-174Article in journal (Refereed) Published##### Abstract [en]

In this article we give an explicit classification for the countably infinite graphs G which are, for some

*k*, ≥*k*-homogeneous. It turns out that a ≥*k*-homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.##### Keywords

>k-homomogeneous, countably infinite graph##### National Category

Algebra and Logic##### Research subject

Mathematical Logic##### Identifiers

urn:nbn:se:uu:diva-329362 (URN)10.1016/j.jctb.2017.08.007 (DOI)000417771100009 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt809",{id:"formSmash:items:resultList:4:j_idt634:5:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt815",{id:"formSmash:items:resultList:4:j_idt634:5:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt821",{id:"formSmash:items:resultList:4:j_idt634:5:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_4_j_idt634_5_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay1144583",{id:"formSmash:items:resultList:4:j_idt634:5:j_idt638",widgetVar:"overlay1144583",target:"formSmash:items:resultList:4:j_idt634:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:partsPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_4_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:4:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_4_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:4:j_idt854:0:fullText"});}); Download (jpg)presentationsbild$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_4_j_idt858_0_j_idt861",{id:"formSmash:items:resultList:4:j_idt858:0:j_idt861",widgetVar:"widget_formSmash_items_resultList_4_j_idt858_0_j_idt861",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:4:j_idt858:0:otherAttachment"});}); Download (pdf)errata$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_4_j_idt858_1_j_idt861",{id:"formSmash:items:resultList:4:j_idt858:1:j_idt861",widgetVar:"widget_formSmash_items_resultList_4_j_idt858_1_j_idt861",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:4:j_idt858:1:otherAttachment"});}); 6. Simple structures axiomatized by almost sure theories Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt591",{id:"formSmash:items:resultList:5:j_idt591",widgetVar:"widget_formSmash_items_resultList_5_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Simple structures axiomatized by almost sure theories2016In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, no 5, p. 435-456Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:5:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_5_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we give a classification of the binary, simple,

*ω*-categorical structures with*SU*-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as*ω*-stability or strong minimality.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_5_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:5:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_5_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:5:j_idt854:0:fullText"});}); 7. To infinity and back Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt591",{id:"formSmash:items:resultList:6:j_idt591",widgetVar:"widget_formSmash_items_resultList_6_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); To infinity and back: Logical limit laws and almost sure theories2014Licentiate thesis, comprehensive summary (Other academic)Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_6_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:6:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_6_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:6:j_idt854:0:fullText"});}); 8. Limit laws and automorphism groups of random nonrigid structures Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt591",{id:"formSmash:items:resultList:7:j_idt591",widgetVar:"widget_formSmash_items_resultList_7_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt594",{id:"formSmash:items:resultList:7:j_idt594",widgetVar:"widget_formSmash_items_resultList_7_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koponen, VeraUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Limit laws and automorphism groups of random nonrigid structures2015In: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, no 2, p. 1-53, article id 1Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:7:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_7_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:7:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_7_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:7:j_idt854:0:fullText"});}); 9. On sets with rank one in simple homogeneous structures Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt591",{id:"formSmash:items:resultList:8:j_idt591",widgetVar:"widget_formSmash_items_resultList_8_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt594",{id:"formSmash:items:resultList:8:j_idt594",widgetVar:"widget_formSmash_items_resultList_8_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koponen, VeraUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On sets with rank one in simple homogeneous structures2015In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, p. 223-250Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:8:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_8_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:8:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_8_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:8:j_idt854:0:fullText"});}); 10. Random l-colourable structures with a pregeometry Ahlman, Ove PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt591",{id:"formSmash:items:resultList:9:j_idt591",widgetVar:"widget_formSmash_items_resultList_9_j_idt591",onLabel:"Ahlman, Ove ",offLabel:"Ahlman, Ove ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt594",{id:"formSmash:items:resultList:9:j_idt594",widgetVar:"widget_formSmash_items_resultList_9_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koponen, VeraUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Random l-colourable structures with a pregeometry2017In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, no 1-2, p. 32-58Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:9:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Classifying Categories Ahlsén, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt591",{id:"formSmash:items:resultList:10:j_idt591",widgetVar:"widget_formSmash_items_resultList_10_j_idt591",onLabel:"Ahlsén, Daniel ",offLabel:"Ahlsén, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_10_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:10:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_10_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:10:j_idt854:0:fullText"});}); 12. Limitless Analysis Ahlsén, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt591",{id:"formSmash:items:resultList:11:j_idt591",widgetVar:"widget_formSmash_items_resultList_11_j_idt591",onLabel:"Ahlsén, Daniel ",offLabel:"Ahlsén, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Limitless Analysis2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_11_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:11:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_11_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:11:j_idt854:0:fullText"});}); 13. Equation Solving in Indian Mathematics Al Homsi, Rania PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt591",{id:"formSmash:items:resultList:12:j_idt591",widgetVar:"widget_formSmash_items_resultList_12_j_idt591",onLabel:"Al Homsi, Rania ",offLabel:"Al Homsi, Rania ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Equation Solving in Indian Mathematics2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_12_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:12:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_12_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:12:j_idt854:0:fullText"});}); 14. Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras Alsaody, Seidon PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt591",{id:"formSmash:items:resultList:13:j_idt591",widgetVar:"widget_formSmash_items_resultList_13_j_idt591",onLabel:"Alsaody, Seidon ",offLabel:"Alsaody, Seidon ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2012Report (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:13:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_13_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A condition for when two eight-dimensional absolute valued algebras are isomorphic was given in [4]. We use this condition to deduce a description (in the sense of Dieterich, [9]) of the category of such algebras, and show how previous descriptions of some full subcategories fit in this description. Led by the structure of these examples, we aim at systematically constructing new subcategories whose classification is manageable. To this end we propose, in greater generality, the definition of sharp stabilizers for group actions, and use these to obtain conditions for when certain subcategories of groupoids are full. This we apply to the category of eight-dimensional absolute valued algebras and obtain a class of subcategories, for which we simplify, and partially solve, the classification problem.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_13_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:13:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_13_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:13:j_idt854:0:fullText"});}); 15. Morphisms in the Category of Finite Dimensional Absolute Valued Algebras Alsaody, Seidon PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt591",{id:"formSmash:items:resultList:14:j_idt591",widgetVar:"widget_formSmash_items_resultList_14_j_idt591",onLabel:"Alsaody, Seidon ",offLabel:"Alsaody, Seidon ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Morphisms in the Category of Finite Dimensional Absolute Valued Algebras2011Report (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:14:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_14_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This is a study of morphisms in the category of nite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classication of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this crosssection.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_14_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:14:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_14_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:14:j_idt854:0:fullText"});}); 16. On Finite-Dimensional Absolute Valued Algebras Alsaody, Seidon PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt591",{id:"formSmash:items:resultList:15:j_idt591",widgetVar:"widget_formSmash_items_resultList_15_j_idt591",onLabel:"Alsaody, Seidon ",offLabel:"Alsaody, Seidon ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On Finite-Dimensional Absolute Valued Algebras2012Licentiate thesis, comprehensive summary (Other academic)Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_15_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:15:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_15_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:15:j_idt854:0:fullText"});}); 17. Knots, Reidemeister Moves and Knot Invariants Alsätra, Tova PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt591",{id:"formSmash:items:resultList:16:j_idt591",widgetVar:"widget_formSmash_items_resultList_16_j_idt591",onLabel:"Alsätra, Tova ",offLabel:"Alsätra, Tova ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Knots, Reidemeister Moves and Knot Invariants2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_16_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:16:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_16_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:16:j_idt854:0:fullText"});}); 18. On second-order generalized quantifiers and finite structures Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt591",{id:"formSmash:items:resultList:17:j_idt591",widgetVar:"widget_formSmash_items_resultList_17_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On second-order generalized quantifiers and finite structures2002In: Ann. Pure Appl. Logic, Vol. 115, no 1-3, p. 1-32Article in journal (Refereed)19. Random sampling of finite graphs with constraints Andersson, Evelina PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt591",{id:"formSmash:items:resultList:18:j_idt591",widgetVar:"widget_formSmash_items_resultList_18_j_idt591",onLabel:"Andersson, Evelina ",offLabel:"Andersson, Evelina ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Random sampling of finite graphs with constraints2014Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_18_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:18:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_18_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:18:j_idt854:0:fullText"});}); Download full text (pdf)appendix$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_18_j_idt854_1_j_idt857",{id:"formSmash:items:resultList:18:j_idt854:1:j_idt857",widgetVar:"widget_formSmash_items_resultList_18_j_idt854_1_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:18:j_idt854:1:fullText"});}); 20. Programming and automating mathematics in the Tarski-Kleene hierarchy Armstrong, Alasdairet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt594",{id:"formSmash:items:resultList:19:j_idt594",widgetVar:"widget_formSmash_items_resultList_19_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Struth, GeorgWeber, TjarkUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Programming and automating mathematics in the Tarski-Kleene hierarchy2014In: Journal of Logical and Algebraic Methods in Programming, ISSN 2352-2208, Vol. 83, no 2, p. 87-102Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:19:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_19_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present examples from a reference implementation of variants of Kleene algebras and Tarski's relation algebras in the theorem proving environment Isabelle/HOL. For Kleene algebras we show how models can be programmed, including sets of traces and paths, languages, binary relations, max-plus and min-plus algebras, matrices, formal power series. For relation algebras we discuss primarily proof automation in a comprehensive library and present an advanced formalisation example.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 21. Linking and Morse Theory Asplund, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt591",{id:"formSmash:items:resultList:20:j_idt591",widgetVar:"widget_formSmash_items_resultList_20_j_idt591",onLabel:"Asplund, Johan ",offLabel:"Asplund, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Linking and Morse Theory2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_20_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:20:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_20_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:20:j_idt854:0:fullText"});}); 22. Extremal Hypergraphs Asplund, Teo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt591",{id:"formSmash:items:resultList:21:j_idt591",widgetVar:"widget_formSmash_items_resultList_21_j_idt591",onLabel:"Asplund, Teo ",offLabel:"Asplund, Teo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Extremal Hypergraphs2013Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_21_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:21:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_21_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:21:j_idt854:0:fullText"});}); 23. Ultrasheaves and double negation Awodey, Steve PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt591",{id:"formSmash:items:resultList:22:j_idt591",widgetVar:"widget_formSmash_items_resultList_22_j_idt591",onLabel:"Awodey, Steve ",offLabel:"Awodey, Steve ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt594",{id:"formSmash:items:resultList:22:j_idt594",widgetVar:"widget_formSmash_items_resultList_22_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Eliasson, JonasPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ultrasheaves and double negation2002Report (Other scientific)24. Ultrasheaves and double negation Awodey, Steveet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt594",{id:"formSmash:items:resultList:23:j_idt594",widgetVar:"widget_formSmash_items_resultList_23_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Eliasson, JonasUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ultrasheaves and double negation2004In: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 45, no 4, p. 235-245Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:23:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_23_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Moerdijk has introduced a topos of sheaves on a category of filters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultrafilters—the

*ultrasheaves*. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on filters.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:23:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 25. Om talet Π Berg, Sandra PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt591",{id:"formSmash:items:resultList:24:j_idt591",widgetVar:"widget_formSmash_items_resultList_24_j_idt591",onLabel:"Berg, Sandra ",offLabel:"Berg, Sandra ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Om talet Π2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_24_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:24:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_24_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:24:j_idt854:0:fullText"});}); 26. Arkimedes metod Berglund, Björn PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt591",{id:"formSmash:items:resultList:25:j_idt591",widgetVar:"widget_formSmash_items_resultList_25_j_idt591",onLabel:"Berglund, Björn ",offLabel:"Berglund, Björn ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Arkimedes metod2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_25_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:25:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_25_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:25:j_idt854:0:fullText"});}); 27. The Unprovability of the Continuum Hypothesis Using the Method of Forcing Bjerkeng van Keppel, Alvar PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt591",{id:"formSmash:items:resultList:26:j_idt591",widgetVar:"widget_formSmash_items_resultList_26_j_idt591",onLabel:"Bjerkeng van Keppel, Alvar ",offLabel:"Bjerkeng van Keppel, Alvar ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The Unprovability of the Continuum Hypothesis Using the Method of Forcing2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_26_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:26:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_26_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:26:j_idt854:0:fullText"});}); 28. Flexible isotopy classification of flexible links Björklund, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt591",{id:"formSmash:items:resultList:27:j_idt591",widgetVar:"widget_formSmash_items_resultList_27_j_idt591",onLabel:"Björklund, Johan ",offLabel:"Björklund, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Flexible isotopy classification of flexible links2016In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, no 8, article id 1650049Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:27:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_27_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we define and study flexible links and flexible isotopy in RP3 subset of CP3. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholm's interpretation of Viro's encomplexed writhe.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:27:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 29. Domain representations of partial functions, with applications to spatial objects and contructive volume geometry Blanck, J PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt591",{id:"formSmash:items:resultList:28:j_idt591",widgetVar:"widget_formSmash_items_resultList_28_j_idt591",onLabel:"Blanck, J ",offLabel:"Blanck, J ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt594",{id:"formSmash:items:resultList:28:j_idt594",widgetVar:"widget_formSmash_items_resultList_28_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stoltenberg-Hansen, VTucker, J.V.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Domain representations of partial functions, with applications to spatial objects and contructive volume geometry2001Report (Other scientific)30. Domain representations of partial functions, with applications to spatial objects and constructive volume geometry Blanck, Jens PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt591",{id:"formSmash:items:resultList:29:j_idt591",widgetVar:"widget_formSmash_items_resultList_29_j_idt591",onLabel:"Blanck, Jens ",offLabel:"Blanck, Jens ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt594",{id:"formSmash:items:resultList:29:j_idt594",widgetVar:"widget_formSmash_items_resultList_29_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stoltenberg-Hansen, ViggoTucker, John V.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Domain representations of partial functions, with applications to spatial objects and constructive volume geometry2002In: Theoret. Comput. Sci., Vol. 284, no 2, p. 207-240Article in journal (Refereed)31. Undecidability of finite satisfiability and characterization of NP in finite model theory Block, Max PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt591",{id:"formSmash:items:resultList:30:j_idt591",widgetVar:"widget_formSmash_items_resultList_30_j_idt591",onLabel:"Block, Max ",offLabel:"Block, Max ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Undecidability of finite satisfiability and characterization of NP in finite model theory2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_30_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:30:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_30_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:30:j_idt854:0:fullText"});}); 32. Miniräknarmania Blomqvist, Christer PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt591",{id:"formSmash:items:resultList:31:j_idt591",widgetVar:"widget_formSmash_items_resultList_31_j_idt591",onLabel:"Blomqvist, Christer ",offLabel:"Blomqvist, Christer ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Miniräknarmania: eller hur att få ut så mycket som möjligt från en enkel reklamräknare2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_31_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:31:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_31_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:31:j_idt854:0:fullText"});}); 33. Localization of Multiscale Screened Poisson Equation Bäck, Viktor PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt591",{id:"formSmash:items:resultList:32:j_idt591",widgetVar:"widget_formSmash_items_resultList_32_j_idt591",onLabel:"Bäck, Viktor ",offLabel:"Bäck, Viktor ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Localization of Multiscale Screened Poisson Equation2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_32_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:32:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_32_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:32:j_idt854:0:fullText"});}); 34. Primtal och kryptografi Carlbaum, Wilhelm PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt591",{id:"formSmash:items:resultList:33:j_idt591",widgetVar:"widget_formSmash_items_resultList_33_j_idt591",onLabel:"Carlbaum, Wilhelm ",offLabel:"Carlbaum, Wilhelm ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Primtal och kryptografi2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisDownload full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_33_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:33:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_33_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:33:j_idt854:0:fullText"});}); 35. Projective modules over classical Lie algebras of infinite rank in the parabolic category Chen, Chih-Whi PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt591",{id:"formSmash:items:resultList:34:j_idt591",widgetVar:"widget_formSmash_items_resultList_34_j_idt591",onLabel:"Chen, Chih-Whi ",offLabel:"Chen, Chih-Whi ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt594",{id:"formSmash:items:resultList:34:j_idt594",widgetVar:"widget_formSmash_items_resultList_34_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lam, NgauNatl Cheng Kung Univ, Dept Math, Tainan 70101, Taiwan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Projective modules over classical Lie algebras of infinite rank in the parabolic category2020In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 224, no 1, p. 125-148Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:34:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_34_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the truncation functors and show the existence of projective cover with a finite Verma flag of each irreducible module in parabolic BGG category O over infinite rank Lie algebra of types a, b, c, d. Moreover, O is a Koszul category. As a consequence, the corresponding parabolic BGG category (O) over bar over infinite rank Lie superalgebra of types a, b, c, d through the super duality is also a Koszul category.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:34:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 36. Affine periplectic Brauer algebras Chen, Chih-Whi PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt591",{id:"formSmash:items:resultList:35:j_idt591",widgetVar:"widget_formSmash_items_resultList_35_j_idt591",onLabel:"Chen, Chih-Whi ",offLabel:"Chen, Chih-Whi ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt594",{id:"formSmash:items:resultList:35:j_idt594",widgetVar:"widget_formSmash_items_resultList_35_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Natl Ctr Theoret Sci, Math Div, Taipei 10617, Taiwan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Peng, Yung-NingNatl Cent Univ, Dept Math, Chungli 32054, Taiwan..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Affine periplectic Brauer algebras2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 501, p. 345-372Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:35:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_35_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We formulate Nazarov-Wenzl type algebras (P) over cap (-)(d) for the representation theory of the periplectic Lie superalgebras p(n). We establish an Arakawa-Suzuki type functor to provide a connection between p(n)-representations and (P) over cap (-)(d)-representations. We also consider various tensor product representations for (P) over cap (-)(d). The periplectic Brauer algebra A(d) developed by Moon is a quotient of (P) over cap (-)(d). In particular, actions induced by Jucys-Murphy elements can also be recovered under the tensor product representation of (P) over cap (-)(d). Moreover, a Poincare-Birkhoff-Witt type basis for (P) over cap (-)(d) is obtained. A diagram realization of PI is also obtained.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:35:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 37. On the kinematic algebra for BCJ numerators beyond the MHV sector Chen, Gang PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt591",{id:"formSmash:items:resultList:36:j_idt591",widgetVar:"widget_formSmash_items_resultList_36_j_idt591",onLabel:"Chen, Gang ",offLabel:"Chen, Gang ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt594",{id:"formSmash:items:resultList:36:j_idt594",widgetVar:"widget_formSmash_items_resultList_36_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Zhejiang Normal Univ, Dept Phys, Jinhua, Zhejiang, Peoples R China;Queen Mary Univ London, Sch Phys & Astron, Ctr Res String Theory, Mile End Rd, London E1 4NS, England.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Johansson, HenrikUppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Stockholm Univ, NORDITA, Roslagstullsbacken 23, S-10691 Stockholm, Sweden;KTH Royal Inst Technol, Roslagstullsbacken 23, S-10691 Stockholm, Sweden.Teng, FeiUppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.Wang, TianhengUppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Nanjing Univ, Dept Phys, Nanjing, Jiangsu, Peoples R China;Humboldt Univ, Inst Phys, Zum Grossen Windkanal 6, D-12489 Berlin, Germany;Humboldt Univ, IRIS Adlershof, Zum Grossen Windkanal 6, D-12489 Berlin, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the kinematic algebra for BCJ numerators beyond the MHV sector2019In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 11, article id 55Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:36:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_36_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ? ((epsilon i .epsilon j )(2)) terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents control the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:36:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_36_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:36:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_36_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:36:j_idt854:0:fullText"});}); 38. Metric boolean algebras and constructive measure theory Coquand, Thieryet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt594",{id:"formSmash:items:resultList:37:j_idt594",widgetVar:"widget_formSmash_items_resultList_37_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Palmgren, ErikUppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Metric boolean algebras and constructive measure theory2002In: Arch. Math. Logic, Vol. 41, p. 687-704Article in journal (Refereed)39. Primitive ideals, twisting functors and star actions for classical Lie superalgebras Coulembier, Kevin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt591",{id:"formSmash:items:resultList:38:j_idt591",widgetVar:"widget_formSmash_items_resultList_38_j_idt591",onLabel:"Coulembier, Kevin ",offLabel:"Coulembier, Kevin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt594",{id:"formSmash:items:resultList:38:j_idt594",widgetVar:"widget_formSmash_items_resultList_38_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Univ Ghent, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Mazorchuk, VolodymyrUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Primitive ideals, twisting functors and star actions for classical Lie superalgebras2016In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 718, p. 207-253Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:38:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_38_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov's twisting functors on the BGG category O. The third topic addresses deformed orbits of the Weyl group. These take over the role of the usual Weyl group orbits for Lie algebras, in the study of primitive ideals and twisting functors for Lie superalgebras.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:38:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 40. The G-Centre and Gradable Derived Equivalences Coulembier, Kevin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt591",{id:"formSmash:items:resultList:39:j_idt591",widgetVar:"widget_formSmash_items_resultList_39_j_idt591",onLabel:"Coulembier, Kevin ",offLabel:"Coulembier, Kevin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt594",{id:"formSmash:items:resultList:39:j_idt594",widgetVar:"widget_formSmash_items_resultList_39_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Mazorchuk, VolodymyrUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The G-Centre and Gradable Derived Equivalences2018In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 105, no 3, p. 289-315Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:39:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_39_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We propose a generalisation for the notion of the centre of an algebra in the setup of algebras graded by an arbitrary abelian group G. Our generalisation, which we call the G-centre, is designed to control the endomorphism category of the grading shift functors. We show that the G-centre is preserved by gradable derived equivalences given by tilting modules. We also discuss links with existing notions in superalgebra theory.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:39:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 41. Indecomposable manipulations with simple modules in category O Coulembier, Kevin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt591",{id:"formSmash:items:resultList:40:j_idt591",widgetVar:"widget_formSmash_items_resultList_40_j_idt591",onLabel:"Coulembier, Kevin ",offLabel:"Coulembier, Kevin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt594",{id:"formSmash:items:resultList:40:j_idt594",widgetVar:"widget_formSmash_items_resultList_40_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Mazorchuk, VolodymyrUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.Zhang, XiaotingUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Indecomposable manipulations with simple modules in category O2019In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 26, no 2, p. 447-499Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:40:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_40_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the problem of indecomposability of translations of simple modules in the principal block of BGG category O for sl(n), as conjectured in [KiM1]. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for n <= 6. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:40:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 42. Legendrian submanifolds with Hamiltonian isotopic symplectizations Courte, Sylvain PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt591",{id:"formSmash:items:resultList:41:j_idt591",widgetVar:"widget_formSmash_items_resultList_41_j_idt591",onLabel:"Courte, Sylvain ",offLabel:"Courte, Sylvain ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Legendrian submanifolds with Hamiltonian isotopic symplectizations2016In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 16, no 6, p. 3641-3652Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:41:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_41_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In any closed contact manifold of dimension at least 1 1, we construct examples of closed Legendrian submanifolds which are not diffeomorphic but whose Lagrangian cylinders in the symplectization are Hamiltonian isotopic.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:41:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 43. Minimal reductions of monomial ideals in dimension two Crispin Quiñonez, Veronica PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt591",{id:"formSmash:items:resultList:42:j_idt591",widgetVar:"widget_formSmash_items_resultList_42_j_idt591",onLabel:"Crispin Quiñonez, Veronica ",offLabel:"Crispin Quiñonez, Veronica ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Minimal reductions of monomial ideals in dimension two2016Report (Refereed)Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_42_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:42:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_42_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:42:j_idt854:0:fullText"});}); 44. On ideals generated by two generic quadratic forms in the exterior algebra Crispin Quiñonez, Veronica PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt591",{id:"formSmash:items:resultList:43:j_idt591",widgetVar:"widget_formSmash_items_resultList_43_j_idt591",onLabel:"Crispin Quiñonez, Veronica ",offLabel:"Crispin Quiñonez, Veronica ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt594",{id:"formSmash:items:resultList:43:j_idt594",widgetVar:"widget_formSmash_items_resultList_43_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lundqvist, SamuelStockholms universitet.Nenashev, GlebMassachusetts Institute of Technology.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On ideals generated by two generic quadratic forms in the exterior algebra2019In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 223, no 12, p. 5067-5082Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:43:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_43_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic quadratic forms. We show that the conjectured series is an upper bound in the coefficient-wise sense, and we determine a majority of the coefficients. We also conjecture that the series is equal to the series of the squarefree polynomial ring modulo the ideal generated by the squares of two generic linear forms.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:43:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 45. Effective Distribution Theory Dahlgren, Fredrik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt591",{id:"formSmash:items:resultList:44:j_idt591",widgetVar:"widget_formSmash_items_resultList_44_j_idt591",onLabel:"Dahlgren, Fredrik ",offLabel:"Dahlgren, Fredrik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Effective Distribution Theory2007Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:44:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_44_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effective domain representations.

To be able to construct effective domain representations of the spaces of test functions considered in distribution theory we need to develop the theory of admissible domain representations over countable pseudobases. This is done in the first paper of the thesis. To construct an effective domain representation of the space of distributions, we introduce and develop a notion of partial continuous function on domains. This is done in the second paper of the thesis. In the third paper we apply the results from the first two papers to develop an effective theory of distributions using effective domains. We prove that the vector space operations on each space, as well as the standard embeddings into the space of distributions effectivise. We also prove that the Fourier transform (as well as its inverse) on the space of tempered distributions is effective. Finally, we show how to use convolution to compute primitives on the space of distributions. In the last paper we investigate the effective properties of a structure theorem for the space of distributions with compact support. We show that each of the four characterisations of the class of compactly supported distributions in the structure theorem gives rise to an effective domain representation of the space. We then use effective reductions (and Turing-reductions) to study the reducibility properties of these four representations. We prove that three of the four representations are effectively equivalent, and furthermore, that all four representations are Turing-equivalent. Finally, we consider a similar structure theorem for the space of distributions supported at 0.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:44:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); List of papers PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt633",{id:"formSmash:items:resultList:44:j_idt633",widgetVar:"widget_formSmash_items_resultList_44_j_idt633",onLabel:"List of papers",offLabel:"List of papers",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 1. Admissible Domain Representations of Inductive Limit SpacesOpen this publication in new window or tab >>Admissible Domain Representations of Inductive Limit Spaces### Dahlgren, Fredrik

Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_0_overlay_some",{id:"formSmash:items:resultList:44:j_idt634:0:overlay:some",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_0_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_0_overlay_otherAuthors",{id:"formSmash:items:resultList:44:j_idt634:0:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_0_overlay_otherAuthors",multiple:true}); In: Mathematical Structures in Computer ScienceArticle in journal (Refereed) Submitted##### Identifiers

urn:nbn:se:uu:diva-96205 (URN)PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt809",{id:"formSmash:items:resultList:44:j_idt634:0:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt815",{id:"formSmash:items:resultList:44:j_idt634:0:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt821",{id:"formSmash:items:resultList:44:j_idt634:0:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_0_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay170702",{id:"formSmash:items:resultList:44:j_idt634:0:j_idt638",widgetVar:"overlay170702",target:"formSmash:items:resultList:44:j_idt634:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 2. Partial Continuous Functions and Admissible Domain RepresentationsOpen this publication in new window or tab >>Partial Continuous Functions and Admissible Domain Representations### Dahlgren, Fredrik

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_1_overlay_some",{id:"formSmash:items:resultList:44:j_idt634:1:overlay:some",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_1_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_1_overlay_otherAuthors",{id:"formSmash:items:resultList:44:j_idt634:1:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_1_overlay_otherAuthors",multiple:true}); 2007 (English)In: Journal of logic and computation (Print), ISSN 0955-792X, E-ISSN 1465-363X, Vol. 17, no 6, p. 1063-1081Article in journal (Refereed) Published##### Abstract [en]

It is well known that to be able to represent continuous functions between domain representable spaces it is critical that the domain representations of the spaces we consider are dense. In this article we show how to develop a representation theory over a category of domains with morphisms partial continuous functions. The raison detre for introducing partial continuous functions is that by passing to partial maps, we are free to consider totalities which are not dense. We show that the category of admissibly representable spaces with morphisms functions which are representable by it partial continuous function is Cartesian closed. Finally, we consider the question of effectivity.

##### National Category

Mathematics##### Identifiers

urn:nbn:se:uu:diva-96206 (URN)10.1093/logcom/exm034 (DOI)000252665100004 ()PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt809",{id:"formSmash:items:resultList:44:j_idt634:1:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt815",{id:"formSmash:items:resultList:44:j_idt634:1:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt821",{id:"formSmash:items:resultList:44:j_idt634:1:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_1_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay170703",{id:"formSmash:items:resultList:44:j_idt634:1:j_idt638",widgetVar:"overlay170703",target:"formSmash:items:resultList:44:j_idt634:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 3. A Domain Theoretic Approach to Effective Distribution TheoryOpen this publication in new window or tab >>A Domain Theoretic Approach to Effective Distribution Theory### Dahlgren, Fredrik

Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_2_overlay_some",{id:"formSmash:items:resultList:44:j_idt634:2:overlay:some",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_2_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_2_overlay_otherAuthors",{id:"formSmash:items:resultList:44:j_idt634:2:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_2_overlay_otherAuthors",multiple:true}); Manuscript (Other academic)##### Identifiers

urn:nbn:se:uu:diva-96207 (URN)PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt809",{id:"formSmash:items:resultList:44:j_idt634:2:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt815",{id:"formSmash:items:resultList:44:j_idt634:2:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt821",{id:"formSmash:items:resultList:44:j_idt634:2:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_2_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay170704",{id:"formSmash:items:resultList:44:j_idt634:2:j_idt638",widgetVar:"overlay170704",target:"formSmash:items:resultList:44:j_idt634:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); 4. Effective Structure Theorems for Spaces of Compactly Supported DistributionsOpen this publication in new window or tab >>Effective Structure Theorems for Spaces of Compactly Supported Distributions### Dahlgren, Fredrik

PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_3_overlay_some",{id:"formSmash:items:resultList:44:j_idt634:3:overlay:some",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_3_overlay_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_3_overlay_otherAuthors",{id:"formSmash:items:resultList:44:j_idt634:3:overlay:otherAuthors",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_3_overlay_otherAuthors",multiple:true}); Manuscript (Other academic)##### Identifiers

urn:nbn:se:uu:diva-96208 (URN)PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt809",{id:"formSmash:items:resultList:44:j_idt634:3:overlay:j_idt809",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt809",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt815",{id:"formSmash:items:resultList:44:j_idt634:3:overlay:j_idt815",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt815",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt821",{id:"formSmash:items:resultList:44:j_idt634:3:overlay:j_idt821",widgetVar:"widget_formSmash_items_resultList_44_j_idt634_3_overlay_j_idt821",multiple:true}); $(function(){PrimeFaces.cw("OverlayPanel","overlay170705",{id:"formSmash:items:resultList:44:j_idt634:3:j_idt638",widgetVar:"overlay170705",target:"formSmash:items:resultList:44:j_idt634:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});}); PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:44:partsPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_44_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:44:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_44_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:44:j_idt854:0:fullText"});}); Download (pdf)COVER01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_44_j_idt858_0_j_idt861",{id:"formSmash:items:resultList:44:j_idt858:0:j_idt861",widgetVar:"widget_formSmash_items_resultList_44_j_idt858_0_j_idt861",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:44:j_idt858:0:otherAttachment"});}); 46. Partial continuous functions and admissible domain representations Dahlgren, Fredrik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt591",{id:"formSmash:items:resultList:45:j_idt591",widgetVar:"widget_formSmash_items_resultList_45_j_idt591",onLabel:"Dahlgren, Fredrik ",offLabel:"Dahlgren, Fredrik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Partial continuous functions and admissible domain representations: Extended abstract2006In: Logical approaches to computational barriers: Proceedings / [ed] Beckmann A; Berger U; Lowe B; Tucker JV, 2006, Vol. 3988, p. 94-104Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:45:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_45_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); It is well known that to be able to represent continuous functions between domain representable spaces it is critical that the domain representations of the spaces we consider are dense. In this article we show how to develop a representation theory over a category of domains with morphisms partial continuous functions. The reason for introducing partial continuous functions is that by passing to partial maps, we are free to consider totalities which are not dense. We show that there is a natural subcategory of the category of representable spaces with morphisms representable maps which is Cartesian closed. Finally, we consider the question of effectivity.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:45:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 47. The double sign of a real division algebra of finite dimension greater than one Darpö, Erik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt591",{id:"formSmash:items:resultList:46:j_idt591",widgetVar:"widget_formSmash_items_resultList_46_j_idt591",onLabel:"Darpö, Erik ",offLabel:"Darpö, Erik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt594",{id:"formSmash:items:resultList:46:j_idt594",widgetVar:"widget_formSmash_items_resultList_46_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Oxford.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dieterich, ErnstUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The double sign of a real division algebra of finite dimension greater than one2011Report (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:46:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_46_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For any real division algebra

*A*of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a E*A*\ {0} are shown to form an invariant of*A*, called its double sign. For each n E {2, 4, 8}, the double sign causes the category Dn of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of Dn.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:46:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_46_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:46:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_46_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:46:j_idt854:0:fullText"});}); 48. The double sign of a real division algebra of finite dimension greater than one Darpö, Eriket al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt594",{id:"formSmash:items:resultList:47:j_idt594",widgetVar:"widget_formSmash_items_resultList_47_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dieterich, ErnstUppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The double sign of a real division algebra of finite dimension greater than one2012In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 285, no 13, p. 1635-1642Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:47:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_47_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a is an element of A\{0} are shown to form an invariant of A, called its double sign. For each n is an element of {2, 4, 8}, the double sign causes the category D-n of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of D-n.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:47:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 49. A general approach to finite dimensional division algebras Dieterich, Ernst PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt591",{id:"formSmash:items:resultList:48:j_idt591",widgetVar:"widget_formSmash_items_resultList_48_j_idt591",onLabel:"Dieterich, Ernst ",offLabel:"Dieterich, Ernst ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A general approach to finite dimensional division algebras2011Report (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:48:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_48_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present a short and rather self-contained introduction to the theory of finite dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In sections 2-3 we develop the general theory over an arbitrary ground field

*k*, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories Dn(k), and the role played by the irreducible morphisms. Sections 4-5 deal with the classical case of real division algebras, emphasizing the double sign decomposition of the level subcategories Dn(R) for n E {2, 4, 8} and the problem of describing their blocks, along with an account of known partial solutions to this problem.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:48:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_48_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:48:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_48_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:48:j_idt854:0:fullText"});}); 50. A general approach to finite dimensional division algebras Dieterich, Ernst PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt591",{id:"formSmash:items:resultList:49:j_idt591",widgetVar:"widget_formSmash_items_resultList_49_j_idt591",onLabel:"Dieterich, Ernst ",offLabel:"Dieterich, Ernst ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A general approach to finite dimensional division algebras2012In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 126, no 1, p. 73-86Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:49:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_49_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present a short and rather self-contained introduction to the theory of finite-dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In Sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories D-n(k), and the role played by the irreducible morphisms. Sections 4-5 deal with the classical case of real division algebras, emphasizing the double sign decomposition of the level subcategories D-n(R) for n is an element of {2, 4, 8} and the problem of describing their blocks, along with an account of known partial solutions to this problem.

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Citation styleapa ieee modern-language-association vancouver Other style $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt929",{id:"formSmash:lower:j_idt929",widgetVar:"widget_formSmash_lower_j_idt929",behaviors:{change:function(ext) {PrimeFaces.ab({s:"formSmash:lower:j_idt929",e:"change",f:"formSmash",p:"formSmash:lower:j_idt929",u:"formSmash:lower:otherStyle"},ext);}}});});

- apa
- ieee
- modern-language-association
- vancouver
- Other style

Languagede-DE en-GB en-US fi-FI nn-NO nn-NB sv-SE Other locale $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt940",{id:"formSmash:lower:j_idt940",widgetVar:"widget_formSmash_lower_j_idt940",behaviors:{change:function(ext) {PrimeFaces.ab({s:"formSmash:lower:j_idt940",e:"change",f:"formSmash",p:"formSmash:lower:j_idt940",u:"formSmash:lower:otherLanguage"},ext);}}});});

- de-DE
- en-GB
- en-US
- fi-FI
- nn-NO
- nn-NB
- sv-SE
- Other locale

Output formathtml text asciidoc rtf $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt950",{id:"formSmash:lower:j_idt950",widgetVar:"widget_formSmash_lower_j_idt950"});});

- html
- text
- asciidoc
- rtf