Results for 'ℵ0‐categorical'

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  1.  28
    ℵ0-categorical structures with a predimension.David M. Evans - 2002 - Annals of Pure and Applied Logic 116 (1-3):157-186.
    We give an axiomatic framework for the non-modular simple 0-categorical structures constructed by Hrushovski. This allows us to verify some of their properties in a uniform way, and to show that these properties are preserved by iterations of the construction.
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  2.  14
    ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  3.  28
    On ℵ0‐categorical weakly circularly minimal structures.Beibut Sh Kulpeshov - 2006 - Mathematical Logic Quarterly 52 (6):555-574.
    We continue exploring analogues of o-minimality and weak o-minimality for circularly ordered sets. The main result is a description of ℵ0-categorical 1-transitive non-primitive weakly circularly minimal structures of convexity rank 1 up to binarity.
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  4.  13
    $aleph_0$-Categorical Modules.Walter Baur - 1975 - Journal of Symbolic Logic 40 (2):213-220.
    It is shown that the first-order theory $\mathrm{Th}_R(A)$ of a countable module over an arbitrary countable ring $R$ is $\aleph_0$-categorical if and only if $A \cong \bigoplus_{t < n}A_i^{(\kappa_i)}, A_i$ finite, $n \in \omega, \kappa_i \leq \omega$. Furthermore, $\mathrm{Th}_R(A)$ is $\aleph_0$-categorical for all $R$-modules $A$ if and only if $R$ is finite and there exist only finitely many isomorphism classes of indecomposable $R$-modules.
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  5.  12
    $aleph_0$-Categorical Tree-Decomposable Structures.A. H. Lachlan - 1992 - Journal of Symbolic Logic 57 (2):501-514.
    Our purpose in this note is to study countable $\aleph_0$-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  6.  43
    On ℵ0-categorical weakly o-minimal structures.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-93.
    0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...)
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  7. On ℵ0-categorical extra-special p-groups.Ulrich Felgner - 1975 - Logique Et Analyse 18 (71-72):407-428.
     
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  8.  4
    ℵ 0 ‐categorical Banach spaces contain ℓp or c 0.Karim Khanaki - 2021 - Mathematical Logic Quarterly 67 (4):469-488.
    This paper has three parts. First, we establish some of the basic model theoretic facts about, the Tsirelson space of Figiel and Johnson [20]. Second, using the results of the first part, we give some facts about general Banach spaces. Third, we study model‐theoretic dividing lines in some Banach spaces and their theories. In particular, we show: (1) has the non independence property (NIP); (2) every Banach space that is ℵ0‐categorical up to small perturbations embeds c0 or () almost (...)
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  9.  70
    ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  10.  19
    ℵ0-categorical structures with arbitrarily fast growth of algebraic closure.David M. Evans & M. E. Pantano - 2002 - Journal of Symbolic Logic 67 (3):897-909.
  11.  11
    ℵ 0 -Categoricity in First-Order Predicate Calculus.Lars Svenonius - 1966 - Journal of Symbolic Logic 31 (3):504-504.
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  12.  43
    Binary types in ℵ0‐categorical weakly o‐minimal theories.Beibut Sh Kulpeshov - 2011 - Mathematical Logic Quarterly 57 (3):246-255.
    Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  13.  53
    ℵ0-categorical tree-decomposable structures.A. H. Lachlan - 1992 - Journal of Symbolic Logic 57 (2):501 - 514.
    Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  14.  19
    ℵ0-categorical modules.Walter Baur - 1975 - Journal of Symbolic Logic 40 (2):213 - 220.
    It is shown that the first-order theory Th R (A) of a countable module over an arbitrary countable ring R is ℵ 0 -categorical if and only if $A \cong \bigoplus_{t finite, n ∈ ω, κ i ≤ ω. Furthermore, Th R (A) is ℵ 0 -categorical for all R-modules A if and only if R is finite and there exist only finitely many isomorphism classes of indecomposable R-modules.
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  15. Nonarithmetical ℵ0-categorical theories with recursive models.Julia F. Knight - 1994 - Journal of Symbolic Logic 59 (1):106 - 112.
  16.  18
    p‐ℵ0‐Categorical Lattice‐Ordered Structures.Carlo Toffalori - 1989 - Mathematical Logic Quarterly 35 (1):23-28.
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  17.  29
    p-ℵ0-Categorical Lattice-Ordered Structures.Carlo Toffalori - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):23-28.
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  18.  28
    On ℵ0-categorical nilrings. II.Gregory Cherlin - 1980 - Journal of Symbolic Logic 45 (2):291 - 301.
    THEOREM. The Jacobson radical of an ℵ 0 -categorical associative ring is nilpotent.
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  19. Coinductive ℵ0-categorical theories.James H. Schmerl - 1990 - Journal of Symbolic Logic 55 (3):1130 - 1137.
  20.  20
    On $aleph_0$-Categorical Nilrings. II.Gregory Cherlin - 1980 - Journal of Symbolic Logic 45 (2):291-301.
    THEOREM. The Jacobson radical of an $\aleph_0$-categorical associative ring is nilpotent.
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  21.  35
    A computable ℵ 0 -categorical structure whose theory computes true arithmetic.Bakhadyr Khoussainov & Antonio Montalbán - 2010 - Journal of Symbolic Logic 75 (2):728-740.
    We construct a computable ℵ0-categorical structure whose first order theory is computably equivalent to the true first order theory of arithmetic.
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  22.  23
    Classifying?0-categorical theories.George Weaver - 1988 - Studia Logica 47 (4):327-345.
    Among the complete ℵ0-categorical theories with finite non-logical vocabularies, we distinguish three classes. The classification is obtained by looking at the number of bound variables needed to isolated complete types. In classI theories, all types are isolated by quantifier free formulas; in classII theories, there is a leastm, greater than zero, s.t. all types are isolated by formulas in no more thanm bound variables: and in classIII theories, for eachm there is a type which cannot be isolated inm or fewer (...)
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  23.  16
    < i> Δ_< sub> 2< sup> 0-categoricity in Boolean algebras and linear orderings.Charles F. D. McCoy - 2003 - Annals of Pure and Applied Logic 119 (1-3):85-120.
  24.  11
    Classification of ℵ0-categorical C-minimal pure C-sets.Françoise Delon & Marie-Hélène Mourgues - 2024 - Annals of Pure and Applied Logic 175 (2):103375.
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  25.  14
    Coinductive $aleph_0$-Categorical Theories.James H. Schmerl - 1990 - Journal of Symbolic Logic 55 (3):1130-1137.
  26. $\aleph\sb 0$-categorical Structures With Arbitrarily Fast Growth Of Algebraic Closure.David Evans & M. E. Pantano - 2002 - Journal of Symbolic Logic 67 (3):897-909.
     
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  27.  13
    Criterion for binarity of ℵ 0 -categorical weakly o-minimal theories.B. Sh Kulpeshov - 2007 - Annals of Pure and Applied Logic 145 (3):354-367.
  28. Decidability and ℵ0-categoricity of theories of partially ordered sets.James H. Schmerl - 1980 - Journal of Symbolic Logic 45 (3):585 - 611.
    This paper is primarily concerned with ℵ 0 -categoricity of theories of partially ordered sets. It contains some general conjectures, a collection of known results and some new theorems on ℵ 0 -categoricity. Among the latter are the following. Corollary 3.3. For every countable ℵ 0 -categorical U there is a linear order of A such that $(\mathfrak{U}, is ℵ 0 -categorical. Corollary 6.7. Every ℵ 0 -categorical theory of a partially ordered set of finite width has a decidable theory. (...)
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  29. Closures in ℵ0-categorical bilinear maps.Andreas Baudisch - 2000 - Journal of Symbolic Logic 65 (2):914 - 922.
    It is possible to define a combinatorial closure on alternating bilinear maps with few relations similar to that in [2]. For the ℵ 0 - categorical case we show that this closure is part of the algebraic closure.
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  30.  23
    On Δ 2 0 -categoricity of equivalence relations.Rod Downey, Alexander G. Melnikov & Keng Meng Ng - 2015 - Annals of Pure and Applied Logic 166 (9):851-880.
  31.  8
    A Class of ℵ0‐Categorical Theories.Anand Pillay - 1981 - Mathematical Logic Quarterly 27 (25‐30):411-418.
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  32.  21
    A Class of ℵ0-Categorical Theories.Anand Pillay - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (25-30):411-418.
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  33.  29
    Automorphism–invariant measures on ℵ0-categorical structures without the independence property.Douglas E. Ensley - 1996 - Journal of Symbolic Logic 61 (2):640 - 652.
    We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of $\operatorname{Aut}(M)$ . This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ 0 -categorical structures without the independence property including those which are stable.
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  34.  16
    Locally p‐ℵ0‐Categorical Theories.Carlo Toffalori - 1986 - Mathematical Logic Quarterly 32 (19‐24):341-348.
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  35.  26
    Locally p-ℵ0-Categorical Theories.Carlo Toffalori - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (19-24):341-348.
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  36.  21
    Characteristically simple ℵ0-categorical groups.Robert H. Gilman - 1984 - Journal of Symbolic Logic 49 (3):900 - 907.
  37.  24
    Lars Svenonius. ℵ0-categoricity in first-order predicate calculus. Theoria , vol. 25 , pp. 82–94.G. Fuhrken - 1966 - Journal of Symbolic Logic 31 (3):504-504.
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  38.  10
    Review: Lars Svenonius, $aleph_0$-Categoricity in First-Order Predicate Calculus. [REVIEW]G. Fuhrken - 1966 - Journal of Symbolic Logic 31 (3):504-504.
  39.  45
    Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets.James H. Schmerl - 1981 - Journal of Symbolic Logic 46 (1):101 - 120.
    Every ℵ 0 -categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ 0 -categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ 0 -categorical partially ordered set not embedding one of them has a decidable theory.
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  40.  56
    Countable homogeneous relational structures and ℵ0-categorical theories.C. Ward Henson - 1972 - Journal of Symbolic Logic 37 (3):494 - 500.
  41.  18
    The Uniqueness of Envelopes in $aleph0$-Categorical, $aleph0$-Stable Structures.James Loveys - 1984 - Journal of Symbolic Logic 49 (4):1171-1184.
  42.  40
    The uniqueness of envelopes in ℵ0-categorical, ℵ0-stable structures.James Loveys - 1984 - Journal of Symbolic Logic 49 (4):1171 - 1184.
  43.  10
    Uri Andrews. A new spectrum of recursive models using an amalgamation construction. The Journal of Symbolic Logic, vol. 73 (2011), no. 3, pp. 883–896. - Bakhadyr Khoussainov and Antonio Montalbán. A computable ℵ 0 -categorical structure whose theory computes true arithmetic. The Journal of Symbolic Logic, vol. 72 (2010), no. 2, pp. 728–740. [REVIEW]Alexander G. Melnikov - 2013 - Bulletin of Symbolic Logic 19 (3):400-401.
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  44.  20
    Baire Categoricity and $\Sigma^{0}_{1}$ -Induction.Stephen G. Simpson - 2014 - Notre Dame Journal of Formal Logic 55 (1):75-78.
  45.  22
    Countably categorical coloured linear orders.Feresiano Mwesigye & John K. Truss - 2010 - Mathematical Logic Quarterly 56 (2):159-163.
    In this paper, we give a classification of ℵ0-categorical coloured linear orders, generalizing Rosenstein's characterization of ℵ0-categorical linear orderings. We show that they can all be built from coloured singletons by concatenation and ℚn-combinations . We give a method using coding trees to describe all structures in our list.
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  46.  16
    On the Categoricity in Power ℵ 0.G. Fuhrken & C. Ryll-Nardzewski - 1966 - Journal of Symbolic Logic 31 (3):505.
  47.  41
    Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
    Let be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS. We prove that for a suitable Hanf number gc0 if χ0 < λ0 λ1, and is categorical inλ1+ then it is categorical in λ0.
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  48.  19
    Punctual Categoricity and Universality.Rod Downey, Noam Greenberg, Alexander Melnikov, Keng Meng Ng & Daniel Turetsky - 2020 - Journal of Symbolic Logic 85 (4):1427-1466.
    We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...)
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  49.  94
    Categoricity in homogeneous complete metric spaces.Åsa Hirvonen & Tapani Hyttinen - 2009 - Archive for Mathematical Logic 48 (3-4):269-322.
    We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which we call the perturbation property. We also assume that the Löwenheim-Skolem number, which in this setting refers to the density character of (...)
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  50.  42
    Categoricity transfer in simple finitary abstract elementary classes.Tapani Hyttinen & Meeri Kesälä - 2011 - Journal of Symbolic Logic 76 (3):759 - 806.
    We continue our study of finitary abstract elementary classes, defined in [7]. In this paper, we prove a categoricity transfer theorem for a case of simple finitary AECs. We introduce the concepts of weak κ-categoricity and f-primary models to the framework of א₀-stable simple finitary AECs with the extension property, whereby we gain the following theorem: Let (������, ≼ ������ ) be a simple finitary AEC, weakly categorical in some uncountable κ. Then (������, ≼ ������ ) is weakly categorical in (...)
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