6 found
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  1.  10
    Constructing an Almost Hyperdefinable Group.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2004 - Journal of Mathematical Logic 4 (02):181-212.
    This paper completes the proof of the group configuration theorem for simple theories started in [1]. We introduce the notion of an almost hyperdefinable structure, and show that it has a reasonable model theory. We then construct an almost hyperdefinable group from a polygroup chunk.
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  2.  4
    Applications of the Group Configuration Theorem in Simple Theories.Ivan Tomašić & Frank O. Wagner - 2003 - Journal of Mathematical Logic 3 (02):239-255.
    We reconstruct the group action in the group configuration theorem. We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular type is locally modular, and the geometry associated to a finitely based locally modular regular type is projective geometry over a finite field.
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  3.  7
    Galois Stratification and ACFA.Ivan Tomašić - 2015 - Annals of Pure and Applied Logic 166 (5):639-663.
  4.  23
    The Group Configuration in Simple Theories and its Applications.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2002 - Bulletin of Symbolic Logic 8 (2):283-298.
    In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or in the $\omega$-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity. The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and (...)
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  5.  23
    The Equality S1 = D = R.Rami Grossberg, Alexei Kolesnikov, Ivan Tomašić & Monica Van Dieren - 2003 - Mathematical Logic Quarterly 49 (2):115-128.
    The new result of this paper is that for θ-stable we have S1[θ] = D[θ, L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the followingMain (...)
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  6.  5
    Direct Twisted Galois Stratification.Ivan Tomašić - 2018 - Annals of Pure and Applied Logic 169 (1):21-53.
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