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  • 1. Cherlin, G.
    et al.
    Djordjevic, Marko
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Hrushovski, E.
    A note on orthogonality and stable embeddedness2005In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 70, no 4, p. 1359-1364Article in journal (Refereed)
    Abstract [en]

    Orthogonality between two stably embedded definable sets is preserved under the addition of constants.

  • 2.
    Djordjevic, Marko
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Finite satisfiability and N-0-categorical structures with trivial dependence2006In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 71, no 3, p. 810-830Article in journal (Refereed)
  • 3.
    Djordjevic, Marko
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Finite variable logic, stability and finite models2001In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 66, no 2, p. 837-858Article in journal (Refereed)
  • 4.
    Djordjevic, Marko
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    On first-order sentences without finite models2004In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 69, no 2, p. 329-339Article in journal (Refereed)
  • 5.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A limit law of almost l-partite graphs2013In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 78, no 3, p. 911-936Article in journal (Refereed)
    Abstract [en]

    For integers l >= 1, d >= 0 we study (undirected) graphs with vertices 1,..., n such that the vertices can be partitioned into l parts such that every vertex has at most d neighbours in its own part. The set of all such graphs is denoted P-n (l, d). We prove a labelled first-order limitlaw, i.e., for every first-order sentence phi, the proportion of graphs in P-n (l, d) that satisfy phi converges as n -> infinity. By combining this result with a result of Hundack, Promel and Steger [12] we also prove that if 1 <= s(1) <=...<= s(1) are integers, then Forb(A(I),s(1),...,s(l)) has alabelled first-order limit law, where Forb (A(I),s(1),...,s(l)) denotes the set of all graphs with vertices 1,..., n, for some n, in which there is no subgraph isomorphic to the complete (l + 1)-partite graph with parts of sizes 1, S-1,..., S-l. In the course of doing this we also prove that there exists a first-order formula depending only on l and d, such that the proportion of g e P (I, d) with the following property approaches 1 as n ->infinity: there is a unique partition of {1,..., n} into l parts such that every vertex has at most d neighbours in its own part, and this partition, viewed as an equivalence relation, is defined by xi.

  • 6.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Binary primitive homogeneous simple structures2017In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 82, no 1, p. 183-207Article in journal (Refereed)
    Abstract [en]

    Suppose that M is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of M is 1 and hence 1-based. It follows that M is a random structure. The conclusion that M is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of omega-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

  • 7.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    On Constraints And Dividing In Ternary Homogeneous Structures2018In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 83, no 4, p. 1691-1721Article in journal (Refereed)
    Abstract [en]

    Let M be ternary, homogeneous and simple. We prove that if M is finitely constrained, then it is supersimple with finite SU-rank and dependence is k-trivial for some k < omega and for finite sets of real elements. Now suppose that, in addition, M is supersimple with SU-rank 1. If M is finitely constrained then algebraic closure in M is trivial. We also find connections between the nature of the constraints of M, the nature of the amalgamations allowed by the age of M, and the nature of definable equivalence relations. A key method of proof is to "extract" constraints (of M) from instances of dividing and from definable equivalence relations. Finally, we give new examples, including an uncountable family, of ternary homogeneous supersimple structures of SU-rank 1.

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