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Search results for 'definability' (try it on Scholar)

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  1. Tapani Hyttinen & Gabriel Sandu (2000). Henkin Quantifiers and the Definability of Truth. Journal of Philosophical Logic 29 (5):507-527.score: 18.0
    Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension $L_{*}^{1}$ (H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close $L_{*}^{1}$ (H) with respect to Boolean operations, and obtain the language L¹(H). At the next level, we consider an extension $L_{*}^{2}$ (H) of L¹(H) in which every sentence is an L¹(H)-sentence prefixed with (...)
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  2. Larisa Maksimova (2006). Definability and Interpolation in Non-Classical Logics. Studia Logica 82 (2):271 - 291.score: 18.0
    Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive (...)
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  3. Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.score: 18.0
    We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier $\sQ_1$ is definable in terms of another quantifier $\sQ_2$, the base logic being monadic second-order logic, reduces to the question if a quantifier $\sQ^{\star}_1$ is definable in $\FO(\sQ^{\star}_2,<,+,\times)$ for certain first-order quantifiers $\sQ^{\star}_1$ and $\sQ^{\star}_2$. We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. In particular, we show that the monadic second-order majority quantifier $\most^1$ (...)
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  4. Ernst Zimmermann (2003). Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12 (1):99-117.score: 18.0
    The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, no general (...)
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  5. Vincent Guingona (2012). On Uniform Definability of Types Over Finite Sets. Journal of Symbolic Logic 77 (2):499-514.score: 18.0
    In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.
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  6. Rohit Parikh (2011). Beth Definability, Interpolation and Language Splitting. Synthese 179 (2):211 - 221.score: 18.0
    Both the Beth definability theorem and Craig's lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L1 with another language L2, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo.Section 3 (...)
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  7. Stanislav O. Speranski (2013). A Note on Definability in Fragments of Arithmetic with Free Unary Predicates. Archive for Mathematical Logic 52 (5-6):507-516.score: 18.0
    We carry out a study of definability issues in the standard models of Presburger and Skolem arithmetics (henceforth referred to simply as Presburger and Skolem arithmetics, for short, because we only deal with these models, not the theories, thus there is no risk of confusion) supplied with free unary predicates—which are strongly related to definability in the monadic SOA (second-order arithmetic) without × or + , respectively. As a consequence, we obtain a very direct proof for ${\Pi^1_1}$ -completeness (...)
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  8. Alexandra Shlapentokh (2001). Diophantine Definability Over Non-Finitely Generated Non-Degenerate Modules of Algebraic Extensions of ℚ. Archive for Mathematical Logic 40 (4):297-328.score: 18.0
    We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be (...)
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  9. Shih Ping Tung (1992). Arithmetic Definability by Formulas with Two Quantifiers. Journal of Symbolic Logic 57 (1):1-11.score: 16.0
    We give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.
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  10. David Fernández Duque (2011). On the Modal Definability of Simulability by Finite Transitive Models. Studia Logica 98 (3):347-373.score: 16.0
    We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language even (...)
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  11. Akito Tsuboi & Saharon Shelah (2002). Definability of Initial Segments. Notre Dame Journal of Formal Logic 43 (2):65-73.score: 16.0
    In any nonstandard model of Peano arithmetic, the standard part is not first-order definable. But we show that in some model the standard part is definable as the unique solution of a formula , where P is a unary predicate variable.
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  12. Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.score: 15.0
    We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.
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  13. Hajnal Andréka, Judit X. Madarász & István Németi (2005). Mutual Definability Does Not Imply Definitional Equivalence, a Simple Example. Mathematical Logic Quarterly 51 (6):591-597.score: 15.0
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  14. Olivier Chapuis & Pascal Koiran (1999). Definability of Geometric Properties in Algebraically Closed Fields. Mathematical Logic Quarterly 45 (4):533-550.score: 15.0
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  15. N. C. A. Da Costa & A. A. M. Rodrigues (2007). Definability and Invariance. Studia Logica 86 (1):1-30.score: 15.0
    In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...)
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  16. Kenji Fukuzaki (2012). Definability of the Ring of Integers in Some Infinite Algebraic Extensions of the Rationals. Mathematical Logic Quarterly 58 (4‐5):317-332.score: 15.0
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  17. T. Lee (2003). Arithmetical Definability Over Finite Structures. Mathematical Logic Quarterly 49 (4):385.score: 15.0
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  18. Larisa Maksimova (2011). Interpolation and Definability Over the Logic Gl. Studia Logica 99 (1-3):249-267.score: 15.0
    In a previous paper [ 21 ] all extensions of Johansson’s minimal logic J with the weak interpolation property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur. In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl (...)
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  19. Hassan Sfouli (2010). Definability and Nondefinability Results for Certain o-Minimal Structures. Mathematical Logic Quarterly 56 (5):503-507.score: 15.0
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  20. Iain A. Stewart (1997). Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second‐Order Logic. Mathematical Logic Quarterly 43 (1):1-21.score: 15.0
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  21. Jon Barwise (1975). Admissible Sets and Structures: An Approach to Definability Theory. Springer-Verlag.score: 15.0
  22. Akito Tsuboi (1992). On Definability of Normal Subgroups of a Superstable Group. Mathematical Logic Quarterly 38 (1):101-106.score: 15.0
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  23. Kentaro Fujimoto (2010). Relative Truth Definability of Axiomatic Truth Theories. Bulletin of Symbolic Logic 16 (3):305-344.score: 12.0
    The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].
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  24. Adonai Sant'Anna, The Definability of Physical Concepts.score: 12.0
    Our main purpose here is to make some considerations about the definability of physical concepts like mass, force, time, space, spacetime, and so on. Our starting motivation is a collection of supposed definitions of closed system in the literature of physics and philosophy of physics. So, we discuss the problem of definitions in theoretical physics from the point of view of modern theories of definition. One of our main conclusions is that there are different kinds of definitions in physics (...)
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  25. Lloyd Humberstone (1998). Note on Supervenience and Definability. Notre Dame Journal of Formal Logic 39 (2):243-252.score: 12.0
    The idea of a property's being supervenient on a class of properties is familiar from much philosophical literature. We give this idea a linguistic turn by converting it into the idea of a predicate symbol's being supervenient on a set of predicate symbols relative to a (first order) theory. What this means is that according to the theory, any individuals differing in respect to whether the given predicate applies to them also differ in respect to the application of at least (...)
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  26. Gabriel Sandu (2000). Minimalism and the Definability of Truth. The Proceedings of the Twentieth World Congress of Philosophy 2000:143-153.score: 12.0
    In this paper I am going to inquire to what extent the main requirements of a minimalist theory of truth and falsity (as formulated, for example, by Horwich and Field) can be consistently implemented in a formal theory. I will discuss several of the existing logical theories of truth, including Tarski-type (un)definability results, Kripke’s partial interpretation of truth and falsity, Barwise and Moss’ theory based upon non-well-founded sets, McGee’s treatment of truth as a vague predicate, and Hintikka’s languages of (...)
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  27. Laureano Luna & William Taylor (2014). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica 22 (2):198-208.score: 12.0
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  28. Joseph Y. Halpern, Dov Samet & Ella Segev (2009). On Definability in Multimodal Logic. Review of Symbolic Logic 2 (3):451-468.score: 12.0
    Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the (...)
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  29. José Iovino (1997). Definability in Functional Analysis. Journal of Symbolic Logic 62 (2):493-505.score: 12.0
    The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of definable real-valued function in functional analysis: a real-valued function f defined on a structure of functional analysis is definable if it can be "approximated" by formulas which do not involve f. We characterize definability of real-valued functions in terms of a purely topological condition which does not involve logic.
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  30. Marius Petria & Răzvan Diaconescu (2006). Abstract Beth Definability in Institutions. Journal of Symbolic Logic 71 (3):1002 - 1028.score: 12.0
    This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new (...)
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  31. Marco Hollenberg (1998). Characterizations of Negative Definability in Modal Logic. Studia Logica 60 (3):357-386.score: 12.0
    Negative definability ([18]) is an alternative way of defining classes of Kripke frames via a modal language, one that enables us, for instance, to define the class of irreflexive frames. Besides a list of closure conditions for negatively definable classes, the paper contains two main theorems. First, a characterization is given of negatively definable classes of (rooted) finite transitive Kripke frames and of such classes defined using both traditional (positive) and negative definitions. Second, we characterize the negatively definable classes (...)
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  32. Eva Hoogland & Maarten Marx (2002). Interpolation and Definability in Guarded Fragments. Studia Logica 70 (3):373 - 409.score: 12.0
    The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in (...)
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  33. A. V. Chagrov & L. A. Chagrova (1995). Algorithmic Problems Concerning First-Order Definability of Modal Formulas on the Class of All Finite Frames. Studia Logica 55 (3):421 - 448.score: 12.0
    The main result is that is no effective algorithmic answer to the question:how to recognize whether arbitrary modal formula has a first-order equivalent on the class of finite frames. Besides, two known problems are solved: it is proved algorithmic undecidability of finite frame consequence between modal formulas; the difference between global and local variants of first-order definability of modal formulas on the class of transitive frames is shown.
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  34. Leo Harrington & Robert I. Soare (1996). Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets. Bulletin of Symbolic Logic 2 (2):199-213.score: 12.0
    We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).
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  35. M. Aiguier & F. Barbier (2007). An Institution-Independent Proof of the Beth Definability Theorem. Studia Logica 85 (3):333 - 359.score: 12.0
    A few results generalizing well-known classical model theory ones have been obtained in institution theory these last two decades (e.g. Craig interpolation, ultraproduct, elementary diagrams). In this paper, we propose a generalized institution-independent version of the Beth definability theorem.
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  36. Keith Simmons (1994). A Paradox of Definability: Richard'S and poincaré'S Ways Out. History and Philosophy of Logic 15 (1):33-44.score: 12.0
    In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian approach.I (...)
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  37. Denis Richard (1989). Definability in Terms of the Successor Function and the Coprimeness Predicate in the Set of Arbitrary Integers. Journal of Symbolic Logic 54 (4):1253-1287.score: 12.0
    Using coding devices based on a theorem due to Zsigmondy, Birkhoff and Vandiver, we first define in terms of successor S and coprimeness predicate $\perp$ a full arithmetic over the set of powers of some fixed prime, then we define in the same terms a restriction of the exponentiation. Hence we prove the main result insuring that all arithmetical relations and functions over prime powers and their opposite are $\{S, \perp\}$ -definable over Z. Applications to definability over Z and (...)
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  38. Michael Benedikt & H. Jerome Keisler (2003). Definability with a Predicate for a Semi-Linear Set. Journal of Symbolic Logic 68 (1):319-351.score: 12.0
    We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small (...)
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  39. Ítala M. L. D'Ottaviano (1987). Definability and Quantifier Elimination for J3-Theories. Studia Logica 46 (1):37 - 54.score: 12.0
    The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J 3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J 3-theories were introduced in the author's doctoral dissertation.
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  40. Luis Fernandez Moreno (1996). Un examen de la argumentación de Frege contra la definibilidad de la verdad (An Examination of Frege's Argumentation Against the Definability of Truth). Theoria 11 (3):165-176.score: 12.0
    La argumentación de Frege contra la definibilidad de la verdad pretende mostrar que una definición de verdad es circular o nos involucra en un regreso al infinito. En la obra de Frege cabe distinguir dos nociones de verdad: la verdad expresada mediante el termine “verdadero” y la verdad expresada mediante la aserción. La argumentación de Frege no muestra que el términe “verdadero” sea indefinible, pero, si se acepta la concepción de Frege acerca de la aserción, de su argumentación, adecuadamente reformulada, (...)
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  41. George Weaver (1994). A Note on Definability in Equational Logic. History and Philosophy of Logic 15 (2):189-199.score: 12.0
    After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications and (...)
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  42. Robert S. Lubarsky (1988). Definability and Initial Segments of C-Degrees. Journal of Symbolic Logic 53 (4):1070-1081.score: 12.0
    We combine two techniques of set theory relating to minimal degrees of constructibility. Jensen constructed a minimal real which is additionally a Π 1 2 singleton. Groszek built an initial segment of order type 1 + α * , for any ordinal α. This paper shows how to force a Π 1 2 singleton such that the c-degrees beneath it, all represented by reals, are of type 1 + α * , for many ordinals α. We also examine the (...) α needs to be so represented by a real. (shrink)
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  43. Douglas E. Miller (1979). An Application of Invariant Sets to Global Definability. Journal of Symbolic Logic 44 (1):9-14.score: 12.0
    Vaught's " * -transform method" is applied to derive a global definability theorem of M. Makkai from a classical theorem of Lusin.
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  44. Anand Pillay (1994). Definability of Types, and Pairs of o-Minimal Structures. Journal of Symbolic Logic 59 (4):1400-1409.score: 12.0
    Let T be a complete O-minimal theory in a language L. We first give an elementary proof of the result (due to Marker and Steinhorn) that all types over Dedekind complete models of T are definable. Let L * be L together with a unary predicate P. Let T * be the L * -theory of all pairs (N, M), where M is a Dedekind complete model of T and N is an |M| + -saturated elementary extension of N (and (...)
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  45. Mihai Prunescu (2002). An Isomorphism Between Monoids of External Embeddings About Definability in Arithmetic. Journal of Symbolic Logic 67 (2):598-620.score: 12.0
    We use a new version of the Definability Theorem of Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.
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  46. Finn V. Jensen (1974). Interpolation and Definability in Abstract Logics. Synthese 27 (1-2):251 - 257.score: 12.0
    A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property implies the weak Beth definability property. An example is given, showing that Beth does not imply Souslin-Kleene.
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  47. Itaï Ben Yaacov (2010). Definability of Groups in ℵ₀-Stable Metric Structures. Journal of Symbolic Logic 75 (3):817-840.score: 12.0
    We prove that in a continuous ℵ₀-stable theory every type-definable group is definable. The two main ingredients in the proof are: 1. Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and 2. Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.
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  48. Byunghan Kim & Rahim Moosa (2007). Stable Definability and Generic Relations. Journal of Symbolic Logic 72 (4):1163 - 1176.score: 12.0
    An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the ϕ-definitions of p as ϕ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably definable (...)
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  49. Luis Fernandez Moreno (1996). Un Examen de la Argumentación de Frege Contra la Definibilidad de la Verdad (an Examination of Frege's Argumentation Against the Definability of Truth). Theoria 11 (3):165-176.score: 12.0
    La argumentación de Frege contra la definibilidad de la verdad pretende mostrar que una definición de verdad es circular o nos involucra en un regreso al infinito. En la obra de Frege cabe distinguir dos nociones de verdad: la verdad expresada mediante el termine “verdadero” y la verdad expresada mediante la aserción. La argumentación de Frege no muestra que el términe “verdadero” sea indefinible, pero, si se acepta la concepción de Frege acerca de la aserción, de su argumentación, adecuadamente reformulada, (...)
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  50. Xavier Caicedo (1990). Definability Properties and the Congruence Closure. Archive for Mathematical Logic 30 (4):231-240.score: 12.0
    We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic (...)
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