Results for 'Model theory'

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  1.  27
    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 (...)
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  2.  4
    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.
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  3.  45
    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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  4. 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 (...)
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  5.  25
    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 (...)
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  6.  10
    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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  7.  8
    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 (...)
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  8.  6
    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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  9.  1
    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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  10.  40
    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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  11.  19
    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 (...)
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  12.  27
    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 (...)
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  13. 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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  14.  11
    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, (...)
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  15.  26
    Model Theory for Infinitary Logic.H. Jerome Keisler - 1971 - Amsterdam: North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  16.  8
    Intuitionistic Logic, Model Theory and Forcing.Melvin Fitting - 1969 - Amsterdam: North-Holland Pub. Co..
  17.  3
    Large Infinitary Languages: Model Theory.M. A. Dickmann - 1975 - American Elsevier Pub. Co..
  18.  16
    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.
  19. Applications of Model Theory to Algebra, Analysis, and Probability.W. A. J. Luxemburg (ed.) - 1969 - New York: Holt, Rinehart and Winston.
     
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  20. Introduction to Model Theory for Leśniewski's Ontology.Zbigniew Stachniak - 1981 - Wydawnictwo Uniwersytetu Wrocłaskiego.
  21.  53
    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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  22.  1
    Model Theory for Modal Logic. Kripke Models for Modal Predicate Calculi.Kenneth A. Bowen - 1981 - Journal of Symbolic Logic 46 (2):415-417.
  23. 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
  24. Model Theory of Infinitary Languages.M. A. Dickmann - 1970 - [Aarhus, Denmark, Universitet, Matematisk Institut].
     
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  25. Model Theory and its Applications.Ralph Kopperman - 1972 - Boston: Allyn & Bacon.
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  26. An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic.Robert Mattison - 1968 - Santa Monica, Calif., Rand.
  27. Some Philosophical Aspects of Abstract Model Theory.Dag Westerståhl - 1976 - Dissertation, University of Gothenburg
     
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  28. 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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  29.  69
    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 (...)
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  30.  54
    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 (...) 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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  31.  5
    On the Implications and Extensions of Luk’s Theory and Model of Scientific Study.Robert Luk - forthcoming - Foundations of Science:1-16.
    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. 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 (...)
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  33.  5
    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 (...)
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  34.  5
    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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  35. 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 (...)
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  36.  11
    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 (...)
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  37.  22
    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 (...)
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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.  25
    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 (...)
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  40.  10
    Model Theory of Measure Spaces and Probability Logic.Rutger Kuyper & Sebastiaan A. Terwijn - 2013 - 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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  41. Being No One: The Self-Model Theory of Subjectivity.Thomas Metzinger - 2003 - MIT Press.
    " In Being No One, Metzinger, a German philosopher, draws strongly on neuroscientific research to present a representationalist and functional analysis of...
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  42.  4
    Arrovian Aggregation of Generalised Expected-Utility Preferences: Possibility Results by Means of Model Theory.Herzberg Frederik - forthcoming - Studia Logica:1-21.
    Cerreia-Vioglio et al. :341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory, is employed.
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  43. The Model Theory of Differential Fields with Finitely Many Commuting Derivations.Tracey McGrail - 2000 - 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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  44. Structuralism, Model Theory and Reduction.Karl-Georg Niebergall - 2002 - 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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  45.  65
    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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  46.  46
    The Craig Interpolation Theorem in Abstract Model Theory.Jouko Väänänen - 2008 - 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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  47.  49
    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 (...)
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  48.  51
    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. 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 (...)
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  50.  46
    Completeness and Categoricity: Frege, Gödel and Model Theory.Stephen Read - 1997 - 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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