Results for 'Model Theory,'

999 found
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  1. Philosophy and Model Theory.Sean Walsh & Tim Button - 2018 - Oxford, UK: Oxford University Press.
    Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.
     
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  2. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - 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 structures, namely, (...)
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  3.  16
    Saturated Model Theory.Gerald E. Sacks - 1972 - Reading, Mass., W. A. Benjamin.
    This book contains the material for a first course in pure model theory with applications to differentially closed fields.
  4.  19
    On the Way to a Wider Model Theory: Completeness Theorems for First-Order Logics of Formal Inconsistency.Walter Carnielli, Marcelo E. Coniglio, Rodrigo Podiacki & Tarcísio Rodrigues - 2014 - Review of Symbolic Logic 7 (3):548-578.
    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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  5.  47
    Uniting Model Theory and the Universalist Tradition of Logic: Carnap’s Early Axiomatics.Iris Loeb - 2014 - 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 the origins and development (...)
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  6.  6
    Positive Model Theory and Amalgamations.Mohammed Belkasmi - 2014 - 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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  7.  44
    Descriptive Inner Model Theory.Grigor Sargsyan - 2013 - 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 for resolving MSC (...)
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  8.  68
    Partial Model Theory as Model Theory.Sebastian Lutz - 2015 - Ergo: An Open Access Journal of Philosophy 2.
    I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of a specific (...)
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  9.  16
    Continuous Model Theory.Chen Chung Chang - 1966 - 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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  10.  45
    Some Applications of Coarse Inner Model Theory.Greg Hjorth - 1997 - 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 to imply (...)
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  11. The Computable Models of Uncountably Categorical Theories – An Inquiry in Recursive Model Theory.Alexander Linsbichler - 2014 - Saarbrücken: AV Akademikerverlag.
    Alex has written an excellent thesis in the area of computable model theory. The latter is a subject that nicely combines model-theoretic ideas with delicate recursiontheoretic constructions. The results demand good knowledge of both fields. In his thesis, Alex begins by reviewing the essential model-theoretic facts, especially the Baldwin-Lachlan result about uncountably categorical theories. This he follows with a brief discussion of recursion theory, including mention of the priority method. The deepest part of the thesis concerns the (...)
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  12.  52
    Mathematical Logic and Model Theory: A Brief Introduction.A. Prestel - 2011 - 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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  13.  62
    The Model Theory of Modules of a C*-Algebra.Camilo Argoty - 2013 - 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 that there is an (...)
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  14.  39
    A Shared Framework for Consequence Operations and Abstract Model Theory.Christian Wallmann - 2013 - 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 present an abstract model-theoretical (...)
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  15. Almost Everywhere Equivalence of Logics in Finite Model Theory.Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto - 1996 - 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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  16.  48
    Finite Model Theory and its Applications.Erich Grädel, Phokion Kolaitis, Libkin G., Marx Leonid, Spencer Maarten, Vardi Joel, Y. Moshe, Yde Venema & Scott Weinstein - 2007 - 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, second-order, fixed-point, and (...)
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  17.  41
    Model Theory for Infinitary Logic.H. Jerome Keisler - 1971 - Amsterdam: North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  18.  19
    Intuitionistic Logic, Model Theory and Forcing.Melvin Fitting - 1969 - Amsterdam: North-Holland Pub. Co..
  19.  14
    Large Infinitary Languages: Model Theory.M. A. Dickmann - 1975 - American Elsevier Pub. Co..
  20.  27
    Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW]Ayda I. Arruda, Newton C. A. Costa & R. Chuaqui (eds.) - 1977 - Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.
  21. Applications of Model Theory to Algebra, Analysis, and Probability.W. A. J. Luxemburg (ed.) - 1969 - New York: Holt, Rinehart and Winston.
  22. Introduction to Model Theory for Leśniewski's Ontology.Zbigniew Stachniak - 1981 - Wydawnictwo Uniwersytetu Wrocłaskiego.
  23. Brains in Vats and Model Theory.Tim Button - forthcoming - 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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  24. Some Philosophical Aspects of Abstract Model Theory.Dag Westerståhl - 1976 - Dissertation, University of Gothenburg
     
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  25. Non-Classical Logics, Model Theory, and Computability Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW]Ayda I. Arruda, R. Chuaqui & Newton C. A. da Costa - 1977
  26. Model Theory of Infinitary Languages.M. A. Dickmann - 1970 - [Aarhus, Denmark, Universitet, Matematisk Institut].
     
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  27.  6
    Model Theory and its Applications.Ralph Kopperman - 1972 - Boston: Allyn & Bacon.
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  28. An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic.Robert Mattison - 1968 - Santa Monica, Calif., Rand.
  29.  13
    Some Elementary Results in Intuitionistic Model Theory.Wim Veldman & Frank Waaldijk - 1996 - Journal of Symbolic Logic 61 (2):745-767.
    We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.
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  30.  12
    Special Model Axiom in Nonstandard Set Theory.Vladimir Kanovei & Michael Reeken - 1999 - 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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  31.  23
    On the Implications and Extensions of Luk’s Theory and Model of Scientific Study.Robert Luk - 2018 - Foundations of Science 23 (1):103-118.
    Recently, Luk tried to establish a model and a theory of scientific studies. He focused on articulating the theory and the model, but he did not emphasize relating them to some issues in philosophy of science. In addition, they might explain some of the issues in philosophy of science, but such explanation is not articulated in his papers. This paper explores the implications and extensions of Luk’s work in philosophy of science or science in general.
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  32.  78
    Non-Local Correlations in Therapeutic Settings? A Qualitative Study on the Basis of Weak Quantum Theory and the Model of Pragmatic Information.Anja Matschuck - 2011 - 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 settings, (...)
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  33.  97
    The Model Theory of M‐Ordered Differential Fields.Cédric Rivière - 2006 - 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 are expanded with (...) 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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  34. The Limits of Representationalism: A Phenomenological Critique of Thomas Metzinger's Self-Model Theory.Sonja Rinofner-Kreidl - 2005 - Synthesis Philosophica (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 refuted as (...)
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  35.  44
    Toward a Model Theory for Transseries.Matthias Aschenbrenner, Lou van den Dries & Joris van der Hoeven - 2013 - 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.
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  36.  13
    Model-Theory of Vector-Spaces Over Unspecified Fields.David Pierce - 2009 - 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 is (...)
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  37.  26
    Positive Model Theory and Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
    We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.
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  38. The Mental Model Theory of Conditionals: A Reply to Guy Politzer.Philip N. Johnson-Laird, Ruth M. J. Byrne & Vittorio Girotto - 2009 - 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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  39. Model Theory and the Philosophy of Mathematical Practice: Formalization Without Foundationalism.John T. Baldwin - 2018 - Cambridge University Press.
    Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the (...)
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  40.  43
    In Defence of (Model) Theory Theory.Heidi Maibom - 2009 - 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 folk psychological knowledge is knowledge of the (...)
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  41.  68
    Some Remarks on the Model Theory of Epistemic Plausibility Models.Lorenz Demey - 2011 - 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 introduce (...)
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  42. Understanding Other Minds: A Criticism of Goldman’s Simulation Theory and an Outline of the Person Model Theory.Albert Newen & Tobias Schlicht - 2009 - 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 register and evaluate persons having mental (...)
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  43.  15
    Naive Probability: A Mental Model Theory of Extensional Reasoning.Philip Johnson-Laird, Paolo Legrenzi, Vittorio Girotto, Maria Sonino Legrenzi & Jean-Paul Caverni - 1999 - Psychological Review 106 (1):62-88.
    This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it (...)
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  44. On the People's Terms: A Republican Theory and Model of Democracy.Philip Pettit - 2012 - Cambridge University Press.
    According to republican theory, we are free persons to the extent that we are protected and secured in the same fundamental choices, on the same public basis, as one another. But there is no public protection or security without a coercive state. Does this mean that any freedom we enjoy is a superficial good that presupposes a deeper, political form of subjection? Philip Pettit addresses this crucial question in On the People's Terms. He argues that state coercion will not involve (...)
  45.  87
    Frege, Hilbert, and the Conceptual Structure of Model Theory.William Demopoulos - 1994 - 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 that (...)
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  46.  7
    The Mental Model Theory of Conditional Reasoning: Critical Appraisal and Revision.Jonathan St B. T. Evans - 1993 - Cognition 48 (1):1-20.
    Johnson-Laird and Byrne present a theory of conditional inference based upon the manipulation of mental models. In the present paper, the theory is critically examined with regard to its ability to account for psychological data, principally with respect to the rate at which people draw the four basic inferences of modus ponens, denial of the antecedent, affirmation of the consequent and modus tollens. It is argued first that the theory is unclear in its definition and in particular with regard to (...)
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  47.  28
    Hilbert, Duality, and the Geometrical Roots of Model Theory.Günther Eder & Georg Schiemer - 2018 - Review of Symbolic Logic 11 (1):48-86.
    The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’sFoundations of Geometry and its mathematical roots in nineteenth-century projective geometry. A central innovation of Hilbert’s book was to provide semantically minded independence proofs for various fragments of Euclidean geometry, thereby contributing to the development of the model-theoretic point of view in logical theory. Though it is generally acknowledged that the development of model theory is intimately bound up with innovations in 19th century geometry, so (...)
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  48.  71
    Language and its Models: Is Model Theory a Theory of Semantics?Jaroslav Peregrin - 1997 - 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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  49.  79
    Some Remarks on the Bearing of Model Theory on the Theory of Theories.William Demopoulos - 2008 - 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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  50.  44
    Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - 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 attempts to develop (...)
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