Search results for 'Model theory' (try it on Scholar)

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  1.  2
    Gerald E. Sacks (1972). Saturated Model Theory. Reading, Mass.,W. A. Benjamin.
    This book contains the material for a first course in pure model theory with applications to differentially closed fields.
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  2.  39
    Thomas Macaulay Ferguson (2012). Notes on the Model Theory of DeMorgan Logics. Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical (...)
  3.  9
    Chen Chung Chang (1966). Continuous Model Theory. Princeton, Princeton University Press.
    CONTINUOUS MODEL THEORY CHAPTER I TOPOLOGICAL PRELIMINARIES. Notation Throughout the monograph our mathematical notation does not differ drastically from ...
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  4.  11
    Iris Loeb (2014). Uniting Model Theory and the Universalist Tradition of Logic: Carnap's Early Axiomatics. Synthese 191 (12):2815-2833.
    We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for (...)
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  5.  8
    Greg Hjorth (1997). Some Applications of Coarse Inner Model Theory. Journal of Symbolic Logic 62 (2):337-365.
    The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown (...)
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  6.  9
    Grigor Sargsyan (2013). Descriptive Inner Model Theory. Bulletin of Symbolic Logic 19 (1):1-55.
    The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture. One particular motivation (...)
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  7.  2
    Walter Carnielli, Marcelo E. Coniglio, Rodrigo Podiacki & Tarcísio Rodrigues (forthcoming). On the Way to a Wider Model Theory: Completeness Theorems for First-Order Logics of Formal Inconsistency. Review of Symbolic Logic:1-31.
    This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent (...)
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  8.  1
    Mohammed Belkasmi (2014). Positive Model Theory and Amalgamations. Notre Dame Journal of Formal Logic 55 (2):205-230.
    We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.
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  9.  37
    A. Prestel (2011). Mathematical Logic and Model Theory: A Brief Introduction. Springer.
    Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...
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  10.  5
    Camilo Argoty (2013). The Model Theory of Modules of a C*-Algebra. Archive for Mathematical Logic 52 (5-6):525-541.
    We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show (...)
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  11.  11
    Christian Wallmann (2013). A Shared Framework for Consequence Operations and Abstract Model Theory. Logica Universalis 7 (2):125-145.
    In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. We (...)
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  12.  60
    Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1996). Almost Everywhere Equivalence of Logics in Finite Model Theory. Bulletin of Symbolic Logic 2 (4):422-443.
    We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...)
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  13.  8
    Erich Grädel, Phokion Kolaitis, Libkin G., Marx Leonid, Spencer Maarten, Vardi Joel, Y. Moshe, Yde Venema & Scott Weinstein (2007). Finite Model Theory and its Applications. Springer.
    This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, (...)
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  14.  17
    H. Jerome Keisler (1971). Model Theory for Infinitary Logic. Amsterdam,North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  15.  1
    Melvin Fitting (1969). Intuitionistic Logic, Model Theory and Forcing. Amsterdam, North-Holland Pub. Co..
  16.  1
    M. A. Dickmann (1975). Large Infinitary Languages: Model Theory. American Elsevier Pub. Co..
  17.  22
    Tim Button (forthcoming). Brains in Vats and Model Theory. In Sanford Goldberg (ed.), The Brain in a Vat. Cambridge University Press
    Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most enduring (...)
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  18. Zbigniew Stachniak (1981). Introduction to Model Theory for Leśniewski's Ontology. Wydawnictwo Uniwersytetu Wrocłaskiego.
  19. W. A. J. Luxemburg (ed.) (1969). Applications of Model Theory to Algebra, Analysis, and Probability. New York, Holt, Rinehart and Winston.
     
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  20.  5
    Ayda I. Arruda, Newton C. A. Costa & R. Chuaqui (eds.) (1977). Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW] Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.
  21. Ayda I. Arruda, R. Chuaqui & Newton C. A. da Costa (1977). Non-Classical Logics, Model Theory, and Computability Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW]
  22.  0
    Kenneth A. Bowen (1981). Model Theory for Modal Logic. Kripke Models for Modal Predicate Calculi. Journal of Symbolic Logic 46 (2):415-417.
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  23. M. A. Dickmann (1970). Model Theory of Infinitary Languages. [Aarhus, Denmark,Universitet, Matematisk Institut].
     
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  24.  0
    Ralph Kopperman (1972). Model Theory and its Applications. Boston,Allyn and Bacon.
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  25. Robert Mattison (1968). An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic. Santa Monica, Calif.,Rand Corp..
  26.  8
    Dag Westerståhl (1976). Some Philosophical Aspects of Abstract Model Theory. Dissertation, University of Gothenburg
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  27.  43
    Cédric Rivière (2006). The Model Theory of M‐Ordered Differential Fields. Mathematical Logic Quarterly 52 (4):331-339.
    In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable .In this paper we study the case where the fields (...) companion by CODFm and give a geometric axiomatization of this theory which uses basic notions of algebraic geometry and some generalized open subsets which appear naturally in this context. This axiomatization allows to recover the one given in [4] for the theory CODF of closed ordered differential fields. Most of the technics we use here are already present in [2] and [4].Finally, we prove that it is possible to describe the completions of CODFm and to obtain quantifier elimination in a slightly enriched language. This generalizes van den Dries' results in the “derivation free” case. (shrink)
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  28.  0
    Vladimir Kanovei & Michael Reeken (1999). Special Model Axiom in Nonstandard Set Theory. Mathematical Logic Quarterly 45 (3):371-384.
    We demonstrate that the special model axiom SMA of Ross admits a natural formalization in Kawai's nonstandard set theory KST but is independent of KST. As an application of our methods to classical model theory, we present a short proof of the consistency of the existence of a k+ like k-saturated model of PA for a given cardinal k.
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  29.  64
    Anja Matschuck (2011). Non-Local Correlations in Therapeutic Settings? A Qualitative Study on the Basis of Weak Quantum Theory and the Model of Pragmatic Information. Axiomathes 21 (2):249-261.
    Weak Quantum Theory (WQT) and the Model of Pragmatic Information (MPI) are two psychophysical concepts developed on the basis of quantum physics. The present study contributes to their empirical examination. The issue of the study is whether WQT and MPI can not only explain ‘psi’-phenomena theoretically but also prove to be consistent with the empirical phenomenology of extrasensory perception (ESP). From the main statements of both models, 33 deductions for psychic readings are derived. Psychic readings are defined as (...)
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  30. Sonja Rinofner-Kreidl (2005). The Limits of Representationalism: A Phenomenological Critique of Thomas Metzinger's Self-Model Theory. Synthesis Philosophica 2 (40):355-371.
    Thomas Metzinger’s self-model theory offers a frame¬work for naturalizing subjective experiences, e.g. first-person perspective. These phenomena are explained by referring to representational contents which are said to be interrelated at diverse levels of consciousness and correlated with brain activities. The paper begins with a consideration on naturalism and anti-naturalism in order to roughly sketch the background of Metzinger’s claim that his theory renders philosophical speculations on the mind unnecessary . In particular, Husserl’s phenomenological conception of consciousness is (...)
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  31.  44
    Philip N. Johnson-Laird, Ruth M. J. Byrne & Vittorio Girotto (2009). The Mental Model Theory of Conditionals: A Reply to Guy Politzer. Topoi 28 (1):75-80.
    This paper replies to Politzer’s ( 2007 ) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.
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  32.  1
    David Pierce (2009). Model-Theory of Vector-Spaces Over Unspecified Fields. Archive for Mathematical Logic 48 (5):421-436.
    Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed fields (...)
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  33.  3
    Matthias Aschenbrenner, Lou van den Dries & Joris van der Hoeven (2013). Toward a Model Theory for Transseries. Notre Dame Journal of Formal Logic 54 (3-4):279-310.
    The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.
  34.  3
    Lorenz Demey (2011). Some Remarks on the Model Theory of Epistemic Plausibility Models. Journal of Applied Non-Classical Logics 21 (3-4):375-395.
    The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then (...)
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  35.  86
    Albert Newen & Tobias Schlicht (2009). Understanding Other Minds: A Criticism of Goldman's Simulation Theory and an Outline of the Person Model Theory. Grazer Philosophische Studien 79 (1):209-242.
    What exactly do we do when we try to make sense of other people e.g. by ascribing mental states like beliefs and desires to them? After a short criticism of Theory-Theory, Interaction Theory and the Narrative Theory of understanding others as well as an extended criticism of the Simulation Theory in Goldman's recent version (2006), we suggest an alternative approach: the Person Model Theory . Person models are the basis for our ability to (...)
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  36.  13
    Georg Schiemer & Erich H. Reck (2013). Logic in the 1930s: Type Theory and Model Theory. Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early (...)
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  37.  12
    Joël Combase (2011). A Silver-Like Perfect Set Theorem with an Application to Borel Model Theory. Notre Dame Journal of Formal Logic 52 (4):415-429.
    A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the (...)
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  38.  8
    Rutger Kuyper & Sebastiaan A. Terwijn (2013). Model Theory of Measure Spaces and Probability Logic. Review of Symbolic Logic 6 (3):367-393.
    We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a (...)
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  39.  10
    Heidi Maibom (2009). In Defence of (Model) Theory Theory. Journal of Consciousness Studies 16 (6-8):6-8.
    In this paper, I present a version of theory theory, so-called model theory, according to which theories are families of models, which represent real-world phenomena when combined with relevant hypotheses, best interpreted in terms of know-how. This form of theory theory has a number of advantages over traditional forms, and is not subject to some recent charges coming from narrativity theory. Most importantly, practice is central to model theory. Practice matters because (...)
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  40.  91
    Karl-Georg Niebergall (2002). Structuralism, Model Theory and Reduction. Synthese 130 (1):135 - 162.
    In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.
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  41.  37
    William Demopoulos (2008). Some Remarks on the Bearing of Model Theory on the Theory of Theories. Synthese 164 (3):359 - 383.
    The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis.
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  42.  26
    William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
    This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert?s Grundlagen der Geometrie to two: (i) Frege?s reliance on what, following Wilfrid Hodges, I call a Frege?Peano language, and (ii) Frege?s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model?theoretic point of view.Moreover, the issues (...)
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  43.  36
    Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
    Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical (...)
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  44.  47
    Tracey McGrail (2000). The Model Theory of Differential Fields with Finitely Many Commuting Derivations. Journal of Symbolic Logic 65 (2):885-913.
    In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ω m + 1.
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  45. Thomas Metzinger (2003). Being No One: The Self-Model Theory of Subjectivity. MIT Press.
    " In Being No One, Metzinger, a German philosopher, draws strongly on neuroscientific research to present a representationalist and functional analysis of...
  46.  31
    Jean-Baptiste Van der Henst (2002). Mental Model Theory Versus the Inference Rule Approach in Relational Reasoning. Thinking and Reasoning 8 (3):193 – 203.
    Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with (...)
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  47.  12
    Sonja Rinofner-Kreidl (2004). Representationalism and Beyond: A Phenomenological Critique of Thomas Metzinger's Self-Model Theory. Journal of Consciousness Studies 11 (10-11):88-108.
    Thomas Metzinger's self-model theory offers a framework for naturalizing subjective experiences, e.g. first-person perspective. These phenomena are explained by referring to representational contents which are said to be interrelated at diverse levels of consciousness and correlated with brain activities. The paper begins with a consideration on naturalism and anti-naturalism in order to roughly sketch the background of Metzinger's claim that his theory renders philosophical speculations on the mind unnecessary. In particular, Husserl's phenomenological conception of consciousness is refuted (...)
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  48.  18
    Jouko Väänänen (2008). The Craig Interpolation Theorem in Abstract Model Theory. Synthese 164 (3):401 - 420.
    The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics (...)
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  49.  34
    Jaroslav Peregrin (1997). Language and its Models: Is Model Theory a Theory of Semantics? Nordic Journal of Philosophical Logic 2 (1):1-23.
    Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.
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  50.  58
    Peter Milne (1999). Tarski, Truth and Model Theory. Proceedings of the Aristotelian Society 99 (2):141–167.
    As Wilfrid Hodges has observed, there is no mention of the notion truth-in-a-model in Tarski's article 'The Concept of Truth in Formalized Languages'; nor does truth make many appearances in his papers on model theory from the early 1950s. In later papers from the same decade, however, this reticence is cast aside. Why should Tarski, who defined truth for formalized languages and pretty much founded model theory, have been so reluctant to speak of truth in (...)
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