Results for 'model theory'

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  1. Classification Theory Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985. [REVIEW]J. T. Baldwin & U. Workshop on Model Theory in Mathematical Logic - 1987
     
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  2.  20
    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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  3.  5
    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 (...)
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  4.  59
    Model Theory for Infinitary Logic: Logic with Countable Conjunctions and Finite Quantifiers.H. Jerome Keisler - 1971 - Amsterdam: North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  5.  4
    Model Theory.Maria Gracia Manzano - 1990 - Oxford, England: Oxford University Press.
    Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.
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  6.  84
    Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
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  7. Models, Model Theory, and Modeling.Michael Glanzberg - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. Cambridge University Press.
     
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  8. Model Theory.C. C. Chang & H. Jerome Keisler - 1992 - Studia Logica 51 (1):154-155.
     
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  9.  23
    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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  10.  28
    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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  11.  53
    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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  12. Model Theory and the 'Factuality' of Semantics.Hilary Putnam - 1989 - In Alexander George (ed.), Reflections on Chomsky. Blackwell. pp. 213--232.
  13.  14
    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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  14. Models, Theories and Concepts: Advanced Nursing Series.James P. Smith - 1994 - Wiley-Blackwell.
    Specially selected articles from the Journal of Advanced Nursing have been updated where appropriate by the original author. Models, Theories and Concepts brings together international authorities in their specialist fields to consider the gaps occurring between theory and practice, as well as the evaluation of a selection of models and emerging theories.
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  15.  61
    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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  16. Model Theory of Infinitary Languages.M. A. Dickmann - 1970 - [Aarhus, Denmark, Universitet, Matematisk Institut].
     
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  17.  21
    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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  18.  90
    Models, Theories, and Language.Jan Faye - 2007 - In Filosofia, scienza e bioetica nel dibattito contemporaneo. Rome: Poligrafico e Zecca dello Stato. pp. 823-838.
    The semantic view on theories has been much in vogue over four decades as the successor of the syntactic view. In the present paper, I take issue with this approach by arguing that theories and models must be separated and that a theory should be considered to be a linguistic systems consisting of a vocabulary and a set of rules for the use of that vocabulary.
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  19. Modal Model Theory.Maarten De Rijke - forthcoming - Annals of Pure and Applied Logic.
  20.  55
    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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  21.  18
    Continuous Model Theory[REVIEW]J. M. P. - 1966 - Review of Metaphysics 20 (2):364-364.
    This monograph is the first really systematic study of the model theory of many-valued logic. The authors develop model theory for systems of logic whose truth-values lie in a compact topological space; the results are analogous to those for two-valued logic—they yield the two valued logics as special cases—but often the methods of proof are more complicated and tend to reveal some of the deep structure of these logics. There is presupposed a fair knowledge of naive (...)
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  22.  19
    Model Theory and Machine Learning.Hunter Chase & James Freitag - 2019 - Bulletin of Symbolic Logic 25 (3):319-332.
    About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. (...)
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  23.  95
    Realism, Model Theory, and Linguistic Semantics.B. Abbott & L. Hauser - unknown
    George Lakoff (in his book Women, Fire, and Dangerous Things(1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name "internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language. This paper examines an argument, given by Lakoff, against realism and (...)
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  24.  40
    Supervenience: Model Theory or Metaphysics?James C. Klagge - 1995 - In Elias E. Savellos & U. Yalcin (eds.), Supervenience: New Essays. Cambridge University Press. pp. 60--72.
  25.  88
    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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  26.  28
    Modal Model Theory.C. C. Chang - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 599--617.
  27.  71
    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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  28. Finite Model Theory and its Applications. Texts in Theoretical Computer Science.E. Grädel, P. G. Kolaitis, L. Libkin, M. Marx, J. Spencer & M. Y. Vardi - 2010 - Bulletin of Symbolic Logic 16 (3):406-407.
  29. Countable Model Theory and Large Cardinals.Harvey Friedman - manuscript
    We can look at this model theoretically as follows. By the linearly ordered predicate calculus, we simply mean ordinary predicate calculus with equality and a special binary relation symbol <. It is required that in all interpretations, < be a linear ordering on the domain. Thus we have the usual completeness theorem provided we add the axioms that assert that < is a linear ordering.
     
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  30.  34
    Husserl, Model Theory, and Formal Essences.Kyle Banick - 2021 - Husserl Studies 37 (2):103-125.
    Husserl’s philosophy of mathematics, his metatheory, and his transcendental phenomenology have a sophisticated and systematic interrelation that remains relevant for questions of ontology today. It is well established that Husserl anticipated many aspects of model theory. I focus on this aspect of Husserl’s philosophy in order to argue that Thomasson’s recent pleonastic reconstruction of Husserl’s approach to essences is incompatible with Husserl’s philosophy as a whole. According to the pleonastic approach, Husserl can appeal to essences in the absence (...)
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  31.  32
    Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
  32.  13
    Some Model Theory of Guarded Negation.Vince Bárány, Michael Benedikt & Balder ten Cate - 2018 - Journal of Symbolic Logic 83 (4):1307-1344.
    The Guarded Negation Fragment is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article (...)
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  33.  52
    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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  34. Model Theory for Modal Logic. Kripke Models for Modal Predicate Calculi.Kenneth A. Bowen - 1983 - Studia Logica 42 (1):105-106.
     
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  35.  20
    The Model Theory of Unitriangular Groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
    he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic (...)
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  36. Realism, Model Theory, and Linguistic Semantics.Larry Hauser - manuscript
    George Lakoff (in his book Women, Fire, and Dangerous Things (1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language.
     
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  37. 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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  38. Basic Model Theory.John Bell - manuscript
    A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...)
     
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  39. Model Theory for Structures Based on Banach Spaces, Abstract of the Talk Given at “X Latin American Symposium on Mathematical Logic”.C. W. Henson - 1996 - Bulletin of Symbolic Logic 2 (2):223-224.
  40. Models, Theories, and Structures: Thirty Years On.Steven French - 2000 - Philosophy of Science 67 (S1):S116 - S127.
    Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated (...)
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  41.  44
    Model Theory of the Regularity and Reflection Schemes.Ali Enayat & Shahram Mohsenipour - 2008 - Archive for Mathematical Logic 47 (5):447-464.
    This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an (...) T in a countable language ${\mathcal{L}}$ with a distinguished linear order:Some model of T has an elementary end extension with a first new element.T ⊢ REF ${(\mathcal{L})}$ .T has an ω 1-like model that continuously embeds ω 1.For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.For some regular uncountable cardinal κ, T has a κ-like model ${\mathfrak{M}}$ that has an elementary extension in which the supremum of M exists.Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to: T has a κ + -like model that continuously embeds a stationary subset of κ. (shrink)
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  42. Which Model Theory ?Philippe De Rouilhan - unknown
     
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  43.  12
    A Model Theory of Modal Reasoning.Victoria A. Bell & P. N. Johnson-Laird - 1998 - Cognitive Science 22 (1):25-51.
    This paper presents a new theory of modal reasoning, i.e. reasoning about what may or may not be the case, and what must or must not be the case. It postulates that individuals construct models of the premises in which they make explicit only what is true. A conclusion is possible if it holds in at least one model, whereas it is necessary if it holds in all the models. The theory makes three predictions, which are corroborated (...)
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  44. Model Theory of Groups and Automorphism Groups.D. M. Evans - 2001 - Studia Logica 67 (1):141-144.
  45. Model Theory Vol. 73.C. C. Chang & H. J. Keisler - 1990 - Elsevier.
     
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  46. Model Theory for Modal Logic—Part II The Elimination of de Re Modality.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):277 - 306.
  47.  18
    Model Theory of Finite Fields and Pseudo-Finite Fields.Zoé Chatzidakis - 1997 - Annals of Pure and Applied Logic 88 (2-3):95-108.
    We give a survey of results obtained in the model theory of finite and pseudo-finite fields.
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  48.  7
    Model Theory of Adeles I.Jamshid Derakhshan & Angus Macintyre - 2022 - Annals of Pure and Applied Logic 173 (3):103074.
  49.  3
    Model Theory of Steiner Triple Systems.Silvia Barbina & Enrique Casanovas - 2019 - Journal of Mathematical Logic 20 (2):2050010.
    A Steiner triple system (STS) is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite STS has a Fraïssé limit M_F. Here, we show that the theory T of M_F is the model completion of the theory of STSs. We also prove that T is not small and it (...)
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  50.  58
    Effective Model Theory Vs. Recursive Model Theory.John Chisholm - 1990 - Journal of Symbolic Logic 55 (3):1168-1191.
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