Results for 'elementary equivalence'

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  1.  29
    On Elementary Equivalence for Equality-Free Logic.E. Casanovas, P. Dellunde & R. Jansana - 1996 - Notre Dame Journal of Formal Logic 37 (3):506-522.
    This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraïssé type theorem. We also give characterizations of elementary classes in equality-free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one.
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  2.  45
    On Elementary Equivalence in Fuzzy Predicate Logics.Pilar Dellunde & Francesc Esteva - 2013 - Archive for Mathematical Logic 52 (1-2):1-17.
    Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863–880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and (...)
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  3.  6
    Elementary Equivalences and Accessible Functors.T. Beke & J. Rosický - 2018 - Annals of Pure and Applied Logic 169 (7):674-703.
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  4.  7
    Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane.Bart Kuijpers, Jan Paredaens & Jan Van Den Bussche - 2000 - Journal of Symbolic Logic 65 (4):1530 - 1555.
    We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.
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  5.  15
    Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups.Francis Oger - 2001 - Journal of Symbolic Logic 66 (3):1471-1480.
    We show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups satisfy a quantifier elimination property. On the other hand, for each integer n, we give some examples of nilpotent groups which satisfy the same sentences with n alternations of quantifiers and do not satisfy the same sentences with n + 1 alternations of quantifiers.
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  6.  40
    Elementary Equivalence of Cσ(K) Spaces for Totally Disconnected, Compact Hausdorff K.S. Heinrich, C. Ward Henson & L. C. Moore - 1986 - Journal of Symbolic Logic 51 (1):135 - 146.
  7.  12
    Condensational Equivalence, Equimorphism, Elementary Equivalence and Similar Similarities.Miloš S. Kurilić & Nenad Morača - 2017 - Annals of Pure and Applied Logic 168 (6):1210-1223.
  8.  41
    Elementary Equivalence of Some Rings of Definable Functions.Vincent Astier - 2008 - Archive for Mathematical Logic 47 (4):327-340.
    We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an (...)
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  9.  25
    On the Elementary Equivalence of Automorphism Groups of Boolean Algebras; Downward Skolem Löwenheim Theorems and Compactness of Related Quantifiers.Matatyahu Rubin & Saharon Shelah - 1980 - Journal of Symbolic Logic 45 (2):265-283.
    THEOREM 1. (⋄ ℵ 1 ) If B is an infinite Boolean algebra (BA), then there is B 1 such that $|\operatorname{Aut} (B_1)| \leq B_1| = \aleph_1$ and $\langle B_1, \operatorname{Aut} (B_1)\rangle \equiv \langle B, \operatorname{Aut}(B)\rangle$ . THEOREM 2. (⋄ ℵ 1 ) There is a countably compact logic stronger than first-order logic even on finite models. This partially answers a question of H. Friedman. These theorems appear in §§ 1 and 2. THEOREM 3. (a) (⋄ ℵ 1 ) If (...)
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  10.  1
    Elementary Equivalence Theorem for Pac Structures.Jan Dobrowolski, Daniel Max Hoffmann & Junguk Lee - 2020 - Journal of Symbolic Logic 85 (4):1467-1498.
    We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism type of their absolute Galois groups. Our results concern two cases: saturated PAC structures and nonsaturated PAC structures.
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  11.  6
    Elementary Equivalence of Infinite-Dimensional Classical Groups.Vladimir Tolstykh - 2000 - Annals of Pure and Applied Logic 105 (1-3):103-156.
    Let D be a division ring such that the number of conjugacy classes of the multiplicative group D ∗ is equal to the power of D ∗ . Suppose that H is the group GL or PGL, where V is a vector space of infinite dimension ϰ over D . We prove, in particular, that, uniformly in κ and D , the first-order theory of H is mutually syntactically interpretable with the theory of the two-sorted structure 〈κ,D〉 in the second-order (...)
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  12.  19
    Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane.Bart Kuijpers, Jan Paredaens & Jan Van den Bussche - 2000 - Journal of Symbolic Logic 65 (4):1530-1555.
    We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.
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  13.  23
    A Note on Elementary Equivalence of C(K) Space.S. Heinrich, C. Ward Henson & L. C. Moore - 1987 - Journal of Symbolic Logic 52 (2):368-373.
  14. An Elementary Notion of Gauge Equivalence.Gordon Belot - 2008 - General Relativity and Gravitation 40 (1):199–215.
    An elementary notion of gauge equivalence is introduced that does not require any Lagrangian or Hamiltonian apparatus. It is shown that in the special case of theories, such as general relativity, whose symmetries can be identified with spacetime diffeomorphisms this elementary notion has many of the same features as the usual notion. In particular, it performs well in the presence of asymptotic boundary conditions.
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  15.  5
    Elementary Equivalence and Constructible Models of Zermelo‐Fraenkel Set Theory.R. H. Cowen - 1976 - Mathematical Logic Quarterly 22 (1):333-338.
  16.  21
    Elementary Equivalence and Constructible Models of Zermelo-Fraenkel Set Theory.R. H. Cowen - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):333-338.
  17. Elementary Equivalence and Decidability for Group-Type Structures Acting on an Abelian Group.P. Simonetta - 1998 - Journal of Symbolic Logic 63 (4):1255-1285.
  18.  6
    Topological Elementary Equivalence of Regular Semi-Algebraic Sets in Three-Dimensional Space.Floris Geerts & Bart Kuijpers - 2018 - Mathematical Logic Quarterly 64 (6):435-463.
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  19. Elementary Equivalence and Isomorphism of Curve Fields on an Algebraically Closed Field.Jl Duret - 1992 - Journal of Symbolic Logic 57 (3):808-823.
  20.  5
    Elementary Equivalence of Rings with Finitely Generated Additive Groups.Alexei G. Myasnikov, Francis Oger & Mahmood Sohrabi - 2018 - Annals of Pure and Applied Logic 169 (6):514-522.
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  21.  26
    Typical Ambiguity and Elementary Equivalence.Daniel Dzierzgowski - 1993 - Mathematical Logic Quarterly 39 (1):436-446.
    A sentence of the usual language of set theory is said to be stratified if it is obtained by “erasing” type indices in a sentence of the language of Russell's Simple Theory of Types. In this paper we give an alternative presentation of a proof the ambiguity theorem stating that any provable stratified sentence has a stratified proof. To this end, we introduce a new set of ambiguity axioms, inspired by Fraïssé's characterization of elementary equivalence; these axioms can (...)
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  22.  4
    Preservation of Elementary Equivalence Under Scalar Extension.Bruce I. Rose - 1982 - Journal of Symbolic Logic 47 (4):734-738.
  23.  5
    Many-Sorted Elementary Equivalence.Daniel Dzierzgowski - 1988 - Notre Dame Journal of Formal Logic 29 (4):530-542.
  24. Complex Multiplication and Elementary Equivalence in the Language of Fields.X. Vidaux - 2002 - Journal of Symbolic Logic 67 (2):635-648.
  25.  30
    A Group-Theoretical Invariant for Elementary Equivalence and its Role in Representations of Elementary Classes.Daniele Mundici - 1981 - Studia Logica 40 (3):253 - 267.
    There is a natural map which assigns to every modelU of typeτ, (U ε Stτ) a groupG (U) in such a way that elementarily equivalent models are mapped into isomorphic groups.G(U) is a subset of a collection whose members are called Fraisse arrows (they are decreasing sequences of sets of partial isomorphisms) and which arise in connection with the Fraisse characterization of elementary equivalence. LetEC λ U be defined as {U εStr τ: ℬ ≡U and |ℬ|=λ; thenEG λ (...)
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  26.  33
    An Elementary Presentation of the Equivalence Between MV-Algebras and L-Groups with Strong Unit.Roberto Cignoli & Daniele Mundici - 1998 - Studia Logica 61 (1):49-64.
    Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.
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  27.  5
    A Topological Zero-One Law and Elementary Equivalence of Finitely Generated Groups.D. Osin - 2021 - Annals of Pure and Applied Logic 172 (3):102915.
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  28.  1
    Ultrafilter Extensions Do Not Preserve Elementary Equivalence.Denis I. Saveliev & Saharon Shelah - 2019 - Mathematical Logic Quarterly 65 (4):511-516.
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  29.  21
    A Language for Category Theory in Which Natural Equivalence Implies Elementary Equivalence of Models.A. Preller - 1985 - Mathematical Logic Quarterly 31 (14‐18):227-234.
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  30.  20
    A Language for Category Theory in Which Natural Equivalence Implies Elementary Equivalence of Models.A. Preller - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (14-18):227-234.
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  31. A Note on Frai'sse's Characterization of Elementary Equivalence.Daniel Dzierzgowski - 1990 - Logique Et Analyse 131 (132):273-286.
  32.  33
    Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras I: Stability. Bulletin of the London Mathematical Society, Vol. 45 , No. 4, Pp. 825–838, Doi:10.1112/Blms/Bdt014. - Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras II: Model Theory. Israel Journal of Mathematics, Vol. 201 , No. 1, Pp. 477–505, Doi:10.1007/S11856-014-1046-7. - Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras III: Elementary Equivalence and II1factors. Bulletin of the London Mathematical Society, Vol. 46 , No. 3, Pp. 609–628, Doi:10.1112/Blms/Bdu012. - Isaac Goldbring, Bradd Hart, and Thomas Sinclair. The Theory of Tracial von Neumann Algebras Does Not Have a Model Companion. Journal of Symbolic Logic, Vol. 78 , No. 3, Pp. 1000–1004. [REVIEW]Itaï Ben Yaacov - 2015 - Bulletin of Symbolic Logic 21 (4):425-427.
  33.  4
    An Arbitrary Equivalence Relation as Elementary Equivalence in an Abstract Logic.Mark E. Nadel - 1980 - Mathematical Logic Quarterly 26 (7‐9):103-109.
  34.  24
    An Arbitrary Equivalence Relation as Elementary Equivalence in an Abstract Logic.Mark E. Nadel - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (7-9):103-109.
  35.  19
    The Equivalence of Different Hierarchies of Elementary Functions.G. T. Herman - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):219-224.
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  36.  4
    The Equivalence of Different Hierarchies of Elementary Functions.G. T. Herman - 1971 - Mathematical Logic Quarterly 17 (1):219-224.
  37.  24
    Abstract Elementary Classes with Löwenheim-Skolem Number Cofinal with Ω.Gregory M. Johnson - 2010 - Notre Dame Journal of Formal Logic 51 (3):361-371.
    In this paper we study abstract elementary classes with Löwenheim-Skolem number $\kappa$ , where $\kappa$ is cofinal with $\omega$ , which have finite character. We generalize results obtained by Kueker for $\kappa=\omega$ . In particular, we show that $\mathbb{K}$ is closed under $L_{\infty,\kappa}$ -elementary equivalence and obtain sufficient conditions for $\mathbb{K}$ to be $L_{\infty,\kappa}$ -axiomatizable. In addition, we provide an example to illustrate that if $\kappa$ is uncountable regular then $\mathbb{K}$ is not closed under $L_{\infty,\kappa}$ -elementary (...)
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  38.  17
    Equivalence to the Continuum Hypothesis of a Certain Proposition of Elementary Plane Geometry.Roy O. Davies - 1962 - Mathematical Logic Quarterly 8 (2):109-111.
  39.  22
    Equivalence to the Continuum Hypothesis of a Certain Proposition of Elementary Plane Geometry.Roy O. Davies - 1962 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 8 (2):109-111.
  40.  3
    Some Elementary Results About the Equivalence of Computability and Decidability.Ulrich Huckenbeck - 1991 - Mathematical Logic Quarterly 37 (5‐6):77-84.
  41.  19
    Some Elementary Results About the Equivalence of Computability and Decidability.Ulrich Huckenbeck - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (5-6):77-84.
  42.  86
    Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive (...)
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  43.  13
    Abstract Elementary Classes and Infinitary Logics.David W. Kueker - 2008 - Annals of Pure and Applied Logic 156 (2):274-286.
    In this paper we study abstract elementary classes using infinitary logics and prove a number of results relating them. For example, if is an a.e.c. with Löwenheim–Skolem number κ then is closed under L∞,κ+-elementary equivalence. If κ=ω and has finite character then is closed under L∞,ω-elementary equivalence. Analogous results are established for . Galois types, saturation, and categoricity are also studied. We prove, for example, that if is finitary and λ-categorical for some infinite λ then (...)
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  44.  55
    Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 2005 - In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. Kings College London Publ.. pp. 17-51.
    In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main (...)
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  45.  11
    Elementary Patterns of Resemblance.Timothy J. Carlson - 2001 - Annals of Pure and Applied Logic 108 (1-3):19-77.
    We will study patterns which occur when considering how Σ 1 -elementary substructures arise within hierarchies of structures. The order in which such patterns evolve will be seen to be independent of the hierarchy of structures provided the hierarchy satisfies some mild conditions. These patterns form the lowest level of what we call patterns of resemblance . They were originally used by the author to verify a conjecture of W. Reinhardt concerning epistemic theories 449–460; Ann. Pure Appl. Logic, to (...)
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  46.  1
    Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 2005 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 17-51.
    In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called \emph{elementary}. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called \emph{canonical}. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main (...)
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  47. Tracks of Relations and Equivalences-Based Reasoning.G. Shtakser & L. Leonenko - 2011 - Studia Logica 97 (3):385-413.
    It is known that the Restricted Predicate Calculus can be embedded in an elementary theory, the signature of which consists of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal adequacy of these models, a question may be posed concerning their conceptual simplicity, "transparency" of interpretations they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called "technical", serving only the (...)
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  48.  32
    On Dualities and Equivalences Between Physical Theories.Jeremy Butterfield - forthcoming - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime. Oxford: Oxford University Press.
    The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall (...)
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  49.  37
    Elementary Differences Between the Degrees of Unsolvability and Degrees of Compressibility.George Barmpalias - 2010 - Annals of Pure and Applied Logic 161 (7):923-934.
    Given two infinite binary sequences A,B we say that B can compress at least as well as A if the prefix-free Kolmogorov complexity relative to B of any binary string is at most as much as the prefix-free Kolmogorov complexity relative to A, modulo a constant. This relation, introduced in Nies [14] and denoted by A≤LKB, is a measure of relative compressing power of oracles, in the same way that Turing reducibility is a measure of relative information. The equivalence (...)
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  50.  3
    The Elementary Classes of Direct and Boolean Products.Daniel Gluschankof - 1994 - Mathematical Logic Quarterly 40 (2):191-203.
    We characterize the elementary classes generated from a distinguished subclass closing by taking direct products and elementary equivalence. In the second part we give the same characterization in terms of atomic Boolean products. In the last part, we study the cases when the class of Boolean products is elementary but is not given by a discriminator.
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