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  1. Some highly saturated models of Peano arithmetic.James H. Schmerl - 2002 - Journal of Symbolic Logic 67 (4):1265-1273.
    Some highly saturated models of Peano Arithmetic are constructed in this paper, which consists of two independent sections. In § 1 we answer a question raised in [10] by constructing some highly saturated, rather classless models of PA. A question raised in [7], [3], ]4] is answered in §2, where highly saturated, nonstandard universes having no bad cuts are constructed.Highly saturated, rather classless models of Peano Arithmetic were constructed in [10]. The main result proved there is the following theorem. If (...)
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  • Elementary properties of the Boolean hull and reduced quotient functors.M. A. Dickmann & F. Miraglia - 2003 - Journal of Symbolic Logic 68 (3):946-971.
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  • Properties of forking in {$ømega$}-free pseudo-algebraically closed fields.Zoé Chatzidakis - 2002 - Journal of Symbolic Logic 67 (3):957-996.
  • Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
    This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel’s incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. (...)
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  • Automorphisms of Finite Order.D. A. Anapolitanos - 1979 - Mathematical Logic Quarterly 25 (33):565-575.
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  • Cyclic Indiscernibles and Skolem Functions.D. A. Anapolitanos - 1981 - Mathematical Logic Quarterly 27 (23-24):353-362.
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  • On the Shadows of Ideals.Adam Piołunowicz - 1987 - Mathematical Logic Quarterly 33 (3):193-197.
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  • Some Theorems on the Lattice of Local Interpretability Types.Jan Krajíček - 1985 - Mathematical Logic Quarterly 31 (29-30):449-460.
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  • Strong Semantical Characterization for Nondeterministic Programs.Laszlo Csirmaz - 1987 - Mathematical Logic Quarterly 33 (5):407-416.
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  • An Algebraic Characterization of Equivalent Preferential Models.Zhaohui Zhu & Rong Zhang - 2007 - Journal of Symbolic Logic 72 (3):803 - 833.
    Preferential model is one of the important semantical structures in nonmonotonic logic. This paper aims to establish an isomorphism theorem for preferential models, which gives us a purely algebraic characterization of the equivalence of preferential models. To this end, we present the notions of local similarity and local simulation. Based on these notions, two operators Δ(·) and μ(·) over preferential models are introduced and explored respectively. Together with other two existent operators ρ(·) and ΠD(·), we introduce an operator ∂D(·). Then (...)
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  • Boolean Valued Models, Boolean Valuations, and Löwenheim-Skolem Theorems.Xinhe Wu - 2023 - Journal of Philosophical Logic 53 (1):293-330.
    Boolean-valued models for first-order languages generalize two-valued models, in that the value range is allowed to be any complete Boolean algebra instead of just the Boolean algebra 2. Boolean-valued models are interesting in multiple aspects: philosophical, logical, and mathematical. The primary goal of this paper is to extend a number of critical model-theoretic notions and to generalize a number of important model-theoretic results based on these notions to Boolean-valued models. For instance, we will investigate (first-order) Boolean valuations, which are natural (...)
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  • Some characterization theorems for infinitary universal horn logic without equality.Pilar Dellunde & Ramon Jansana - 1996 - Journal of Symbolic Logic 61 (4):1242-1260.
    In this paper we mainly study preservation theorems for two fragments of the infinitary languagesLκκ, withκregular, without the equality symbol: the universal Horn fragment and the universal strict Horn fragment. In particular, whenκisω, we obtain the corresponding theorems for the first-order case.The universal Horn fragment of first-order logic (with equality) has been extensively studied; for references see [10], [7] and [8]. But the universal Horn fragment without equality, used frequently in logic programming, has received much less attention from the model (...)
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  • Expressivity in polygonal, plane mereotopology.Ian Pratt & Dominik Schoop - 2000 - Journal of Symbolic Logic 65 (2):822-838.
    In recent years, there has been renewed interest in the development of formal languages for describing mereological (part-whole) and topological relationships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as ‘xis connected’ or ‘xis a part ofy’, and the entities over which their variables range are, accordingly, notpoints, butregions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers two first-order mereotopological languages, and (...)
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  • Modèles saturés et modèles engendrés par des indiscernables.Benoît Mariou - 2001 - Journal of Symbolic Logic 66 (1):325-348.
    In the early eighties, answering a question of A. Macintyre, J. H. Schmerl ([13]) proved that every countable recursively saturated structure, equipped with a functionβencoding the finite functions, is theβ-closure of an infinite indiscernible sequence. This result implies that every countably saturated structure, in a countable but not necessarily recursive language, is an Ehrenfeucht-Mostowski model, by which we mean that the structureexpands, in a countable language, to the Skolem hull of an infinite indiscernible sequence (in the new language).More recently, D. (...)
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  • Automorphisms moving all non-algebraic points and an application to NF.Friederike Körner - 1998 - Journal of Symbolic Logic 63 (3):815-830.
    Section 1 is devoted to the study of countable recursively saturated models with an automorphism moving every non-algebraic point. We show that every countable theory has such a model and exhibit necessary and sufficient conditions for the existence of automorphisms moving all non-algebraic points. Furthermore we show that there are many complete theories with the property that every countable recursively saturated model has such an automorphism.In Section 2 we apply our main theorem from Section 1 to models of Quine's set (...)
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  • Branching-time logic with quantification over branches: The point of view of modal logic.Alberto Zanardo - 1996 - Journal of Symbolic Logic 61 (1):1-39.
    In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) (...)
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  • The fundamental theorem of ultraproduct in Pavelka's logic.Mingsheng Ying - 1992 - Mathematical Logic Quarterly 38 (1):197-201.
    In [This Zeitschrift 25 , 45-52, 119-134, 447-464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order Pavelka's logic is preserved (...)
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  • Compactness, the löwenheim-Skolem property and the direct product of lattices of truth values.Mingsheng Ying - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):521-524.
  • Could experience disconfirm the propositions of arithmetic?Jessica M. Wilson - 2000 - Canadian Journal of Philosophy 30 (1):55--84.
    Alberto Casullo ("Necessity, Certainty, and the A Priori", Canadian Journal of Philosophy 18, 1988) argues that arithmetical propositions could be disconfirmed by appeal to an invented scenario, wherein our standard counting procedures indicate that 2 + 2 != 4. Our best response to such a scenario would be, Casullo suggests, to accept the results of the counting procedures, and give up standard arithmetic. While Casullo's scenario avoids arguments against previous "disconfirming" scenarios, it founders on the assumption, common to scenario and (...)
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  • A Note on Products and Degree of Types.J. Wierzejewski - 1976 - Mathematical Logic Quarterly 23 (27‐30):431-434.
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  • A Note on Products and Degree of Types.J. Wierzejewski - 1977 - Mathematical Logic Quarterly 23 (27-30):431-434.
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  • Model theory of strictly upper triangular matrix rings.William H. Wheeler - 1980 - Journal of Symbolic Logic 45 (3):455-463.
  • Boolean universes above Boolean models.Friedrich Wehrung - 1993 - Journal of Symbolic Logic 58 (4):1219-1250.
    We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are "boundedly algebraically compact" in the language $(+,-,\cdot,\wedge,\vee,\leq)$ , and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any (...)
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  • Back and forth constructions in modal logic: An interpolation theorem for a family of modal logics.George Weaver & Jeffrey Welaish - 1986 - Journal of Symbolic Logic 51 (4):969-980.
  • A Note on the Interpolation Theorem in First Order Logic.George Weaver - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):215-218.
  • An Algebraic Proof of Completeness for Monadic Fuzzy Predicate Logic.Jun Tao Wang & Hongwei Wu - forthcoming - Review of Symbolic Logic:1-27.
    Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The main (...)
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  • Theories of modules closed under direct products.Roger Villemaire - 1992 - Journal of Symbolic Logic 57 (2):515-521.
    We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$.
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  • The two-cardinal problem for languages of arbitrary cardinality.Luis Miguel & Villegas Silva - 2010 - Journal of Symbolic Logic 75 (3):785-801.
    Let ℒ be a first-order language of cardinality κ++ with a distinguished unary predicate symbol U. In this paper we prove, working on L, the two cardinal transfer theorem (κ⁺,κ) ⇒ (κ++,κ⁺) for this language. This problem was posed by Chang and Keisler more than twenty years ago.
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  • Alfred Tarski's work in model theory.Robert L. Vaught - 1986 - Journal of Symbolic Logic 51 (4):869-882.
  • Uniform interpolation and compact congruences.Samuel J. van Gool, George Metcalfe & Constantine Tsinakis - 2017 - Annals of Pure and Applied Logic 168 (10):1927-1948.
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  • The Logical Study of Science.Johan van Benthem - 1982 - Synthese 51 (3):431-472.
    The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously -- having to do, amongst other things, with different "scientific mentalities" in the two disciplines. Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion (...)
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  • One or Two Gentle Remarks about Hans Halvorson’s Critique of the Semantic View.Bas C. van Fraassen - 2014 - Philosophy of Science 81 (2):276-283,.
    In recent papers Hans Halvorson has offered a critique of the semantic view of theories, showing that theories may be the same although the corresponding sets of models are different and, conversely, that theories may be different although the corresponding sets of models are the same. This critique will be assessed, first, as it pertains to issues concerning scientific models in the empirical sciences and, second, independent of any concern with empirical science.
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  • Logic of transition systems.Johan Van Benthem & Jan Bergstra - 1994 - Journal of Logic, Language and Information 3 (4):247-283.
    Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this (...)
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  • Alfred Tarski's elimination theory for real closed fields.Lou Van Den Dries - 1988 - Journal of Symbolic Logic 53 (1):7-19.
  • Finite Undecidability in Nip Fields.Brian Tyrrell - forthcoming - Journal of Symbolic Logic:1-24.
    A field K in a ring language $\mathcal {L}$ is finitely undecidable if $\mbox {Cons}(T)$ is undecidable for every nonempty finite $T \subseteq {\mathtt{Th}}(K; \mathcal {L})$. We extend a construction of Ziegler and (among other results) use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially valued field is finitely undecidable. We conclude (assuming the NIP Fields Conjecture) that every NIP field is finitely undecidable. This work is drawn from the author’s PhD thesis [48, Chapter 3].
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  • On theories having a finite number of nonisomorphic countable models.Akito Tsuboi - 1985 - Journal of Symbolic Logic 50 (3):806-808.
  • Nonstandard methods for finite structures.Akito Tsuboi - 2020 - Mathematical Logic Quarterly 66 (3):367-372.
    We discuss the possibility of applying the compactness theorem to the study of finite structures. Given a class of finite structures, it is important to determine whether it can be expressed by a particular category of sentences. We are interested in this type of problem, and use nonstandard method for showing the non‐expressibility of certain classes of finite graphs by an existential monadic second order sentence.
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  • Contributions to the Theory of Semisets IV.Petr Štêpánek - 1974 - Mathematical Logic Quarterly 20 (23‐24):373-384.
  • Model completeness and direct power.Kazem Taghva - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (1):3-9.
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  • On the generator problem.Wieslaw Szwast - 1990 - Mathematical Logic Quarterly 36 (1):23-27.
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  • Interpretations With Parameters.L. W. Szczerba - 1980 - Mathematical Logic Quarterly 26 (1-6):35-39.
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  • Why There is no General Solution to the Problem of Software Verification.John Symons & Jack K. Horner - 2020 - Foundations of Science 25 (3):541-557.
    How can we be certain that software is reliable? Is there any method that can verify the correctness of software for all cases of interest? Computer scientists and software engineers have informally assumed that there is no fully general solution to the verification problem. In this paper, we survey approaches to the problem of software verification and offer a new proof for why there can be no general solution.
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  • Why There is no General Solution to the Problem of Software Verification.John Symons & Jack J. Horner - 2020 - Foundations of Science 25 (3):541-557.
    How can we be certain that software is reliable? Is there any method that can verify the correctness of software for all cases of interest? Computer scientists and software engineers have informally assumed that there is no fully general solution to the verification problem. In this paper, we survey approaches to the problem of software verification and offer a new proof for why there can be no general solution.
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  • The Representational Semantic Conception.Mauricio Suárez & Francesca Pero - 2019 - Philosophy of Science 86 (2):344-365.
    This paper argues for a representational semantic conception of scientific theories, which respects the bare claim of any semantic view, namely that theories can be characterised as sets of models. RSC must be sharply distinguished from structural versions that assume a further identity of ‘models’ and ‘structures’, which we reject. The practice-turn in the recent philosophical literature suggests instead that modelling must be understood in a deflationary spirit, in terms of the diverse representational practices in the sciences. These insights are (...)
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  • Deflationary representation, inference, and practice.Mauricio Suárez - 2015 - Studies in History and Philosophy of Science Part A 49 (C):36-47.
    This paper defends the deflationary character of two recent views regarding scientific representation, namely RIG Hughes’ DDI model and the inferential conception. It is first argued that these views’ deflationism is akin to the homonymous position in discussions regarding the nature of truth. There, we are invited to consider the platitudes that the predicate “true” obeys at the level of practice, disregarding any deeper, or more substantive, account of its nature. More generally, for any concept X, a deflationary approach is (...)
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  • Ultrapowers without the axiom of choice.Mitchell Spector - 1988 - Journal of Symbolic Logic 53 (4):1208-1219.
    A new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice fails; this (...)
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  • Model theory under the axiom of determinateness.Mitchell Spector - 1985 - Journal of Symbolic Logic 50 (3):773-780.
    We initiate the study of model theory in the absence of the Axiom of Choice, using the Axiom of Determinateness as a powerful substitute. We first show that, in this context, L ω 1 ω is no more powerful than first-order logic. The emphasis then turns to upward Lowenhein-Skolem theorems; ℵ 1 is the Hanf number of first-order logic, of L ω 1 ω , and of a strong fragment of L ω 1 ω . The main technical innovation is (...)
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  • An addendum to Demopoulos and Friedman (1985).Graham Solomon - 1989 - Philosophy of Science 56 (3):497-501.
    M. H. A. Newman (1928) criticized Russell's structuralist philosophy of science. Demopoulos and Friedman have discussed Newman's critique, showing its relevance to the structuralist positions held by Schlick and Carnap, and to Putnam's argument against "metaphysical realism". I discuss Richard Braithwaite's (1940) appeal to Newman in a critique of Arthur Eddington. Braithwaite believed Newman had shown that "structure depends upon content". Eddington, in his reply, misunderstood the generality of Newman's argument.
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  • Omitting models.Ernest Snapper - 1977 - Journal of Symbolic Logic 42 (1):29-32.
  • Bowtie‐free graphs and generic automorphisms.Daoud Siniora - 2023 - Mathematical Logic Quarterly 69 (2):221-230.
    We show that the countable universal ω‐categorical bowtie‐free graph admits generic automorphisms. Moreover, we show that this graph is not finitely homogenisable.
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