uu.seUppsala University Publications

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Independence and the finite submodel propertyPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 158, no 1-2, 58-79 p.Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier , 2009. Vol. 158, no 1-2, 58-79 p.
##### Keyword [en]

model theory, independence, finite submodel property, random structure
##### National Category

Mathematics
##### Research subject

Mathematical Logic
##### Identifiers

URN: urn:nbn:se:uu:diva-119671DOI: 10.1016/j.apal.2008.10.004ISI: 000264661900004OAI: oai:DiVA.org:uu-119671DiVA: diva2:300630
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Available from: 2010-02-26 Created: 2010-02-26 Last updated: 2017-12-12Bibliographically approved

We study a class c of aleph(0)-categorical simple structures such that every M in c has uncomplicated forking behavior and such that definable relations in M which do not cause forking are independent in a sense that is made precise; we call structures in c independent. The SU-rank of such M may be n for any natural number n > 0. The most well-known unstable member of c is the random graph, which has SU-rank one. The main result is that for every strongly independent structure M in e, if a sentence phi is true in M then phi is true in a finite substructure of M. The same conclusion holds for every structure in c with SU-rank one: so in this case the word 'strongly' can be removed. A probability theoretic argument is involved and it requires sufficient independence between relations which do not cause forking. A stable structure M belongs to c if and only if it is aleph(0)-categorical, aleph(0)-stable and every definable strictly minimal Subset of M-eq is indiscernible.

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