18 found
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  1.  13
    Stationarily Ordered Types and the Number of Countable Models.Slavko Moconja & Predrag Tanović - 2020 - Annals of Pure and Applied Logic 171 (3):102765.
    We introduce the notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the former is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary relation on elements realizing stationarily ordered types, is an equivalence relation and that each stationarily ordered type in a model determines some order-type as an invariant of the model. We study weak and forking non-orthogonality of stationarily ordered types, show that (...)
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  2.  20
    On Constants and the Strict Order Property.Predrag Tanović - 2006 - Archive for Mathematical Logic 45 (4):423-430.
    Let T be a complete, countable, first-order theory with a finite number of countable models. Assuming that dcl(∅) is infinite we show that T has the strict order property.
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  3.  10
    Generically Stable Regular Types.Predrag Tanović - 2015 - Journal of Symbolic Logic 80 (1):308-321.
  4.  22
    Types Directed by Constants.Predrag Tanović - 2010 - Annals of Pure and Applied Logic 161 (7):944-955.
    Let T be a complete, countable, first-order theory having infinite models. We introduce types directed by constants, and prove that their presence in a model of T guaranties the maximal number of non-isomorphic countable models : I=2.
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  5.  23
    Minimal First-Order Structures.Predrag Tanović - 2011 - Annals of Pure and Applied Logic 162 (11):948-957.
    We prove a dichotomy theorem for minimal structures and use it to prove that the number of non-isomorphic countable elementary extensions of an arbitrary countable, infinite first-order structure is infinite.
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  6.  19
    Asymmetric Regular Types.Slavko Moconja & Predrag Tanović - 2015 - Annals of Pure and Applied Logic 166 (2):93-120.
  7. Countable Models of Trivial Theories Which Admit Finite Coding.James Loveys & Predrag Tanović - 1996 - Journal of Symbolic Logic 61 (4):1279-1286.
    We prove: Theorem. A complete first order theory in a countable language which is strictly stable, trivial and which admits finite coding has 2 ℵ 0 nonisomorphic countable models. Combined with the corresponding result or superstable theories from [4] our result confirms the Vaught conjecture for trivial theories which admit finite coding.
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  8.  5
    Theories with Constants and Three Countable Models.Predrag Tanović - 2007 - Archive for Mathematical Logic 46 (5-6):517-527.
    We prove that a countable, complete, first-order theory with infinite dcl( $ \theta $ ) and precisely three non-isomorphic countable models interprets a variant of Ehrenfeucht’s or Peretyatkin’s example.
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  9.  9
    Asymmetric RK-Minimal Types.Predrag Tanović - 2010 - Archive for Mathematical Logic 49 (3):367-377.
    We consider semi-isolation on the locus of a strongly non-isolated, RK-minimal type in a small theory, and we prove that its asymmetry (as a binary relation) is caused by a specific form of the strict order property: the partial definability of semi-isolation.
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  10.  3
    Non-Isolated Types in Stable Theories.Predrag Tanović - 2007 - Annals of Pure and Applied Logic 145 (1):1-15.
    We introduce notions of strong and eventual strong non-isolation for types in countable, stable theories. For T superstable or small stable we prove a dichotomy theorem: a regular type over a finite domain is either eventually strongly non-isolated or is non-orthogonal to a NENI type . As an application we obtain the upper bound for Lascar’s rank of a superstable theory which is one-based or trivial, and has fewer than 20 non-isomorphic countable models.
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  11. A Definable Continuous Rank for Nonmultidimensional Superstable Theories.Ambar Chowdhury, James Loveys & Predrag Tanović - 1996 - Journal of Symbolic Logic 61 (3):967-984.
  12.  14
    A Note on a-Prime Models.Bradd Hart, Željko Sokolović & Predrag Tanovic - 1999 - Journal of Symbolic Logic 64 (4):1557-1562.
    We answer a question of Cassidy and Kolchin about the universality of the constrained closure of a differential field by working in a larger category of models.
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  13.  6
    Semi-Isolation and the Strict Order Property.Sergey Sudoplatov & Predrag Tanović - 2015 - Notre Dame Journal of Formal Logic 56 (4):555-572.
    We study semi-isolation as a binary relation on the locus of a complete type and prove that—under some additional assumptions—it induces the strict order property.
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  14.  3
    A Note on Countable Models of 1-Based Theories.Predrag Tanovic - 2002 - Archive for Mathematical Logic 41 (7):669-671.
    We prove that the existence of a nonisolated type having a finite domain and which is orthogonal to øin a 1-based theory implies that it has a continuum nonisomorphic countable models.
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  15.  1
    Around Rubin’s “Theories of Linear Order”.Predrag Tanović, Slavko Moconja & Dejan Ilić - 2020 - Journal of Symbolic Logic 85 (4):1403-1426.
    Let $\mathcal M=$ be a linearly ordered first-order structure and T its complete theory. We investigate conditions for T that could guarantee that $\mathcal M$ is not much more complex than some colored orders. Motivated by Rubin’s work [5], we label three conditions expressing properties of types of T and/or automorphisms of models of T. We prove several results which indicate the “geometric” simplicity of definable sets in models of theories satisfying these conditions. For example, we prove that the strongest (...)
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  16.  7
    On Definability of Types of Finite Cantor-Bendixson Rank.Predrag Tanovic - 2011 - Mathematical Logic Quarterly 57 (3):256-260.
    We prove that every type of finite Cantor-Bendixson rank over a model of a first-order theory without the strict order property is definable and has a unique nonforking extension to a global type. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  17. On Kueker's Conjecture.Predrag Tanović - 2012 - Journal of Symbolic Logic 77 (4):1245-1256.
    We prove that a Kueker theory with infinite dcl(Ø) does not have the strict order property and that strongly minimal types are dense: any non-algebraic formula is contained in a strongly minimal type.
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  18.  25
    Simple Groups and the Number of Countable Models.Predrag Tanović - 2013 - Archive for Mathematical Logic 52 (7-8):779-791.
    Let T be a complete, superstable theory with fewer than ${2^{\aleph_{0}}}$ countable models. Assuming that generic types of infinite, simple groups definable in T eq are sufficiently non-isolated we prove that ω ω is the strict upper bound for the Lascar rank of T.
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