The Theory of Models

The Theory of Models

Proceedings of the 1963 International Symposium at Berkeley

1st Edition - January 1, 1963

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  • Editors: J.W. Addison, Leon Henkin, Alfred Tarski
  • eBook ISBN: 9781483275345

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Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.

Table of Contents

  • Dedication


    List of Papers Grouped by Subject Matter

    Foreword on Terminology

    Invited Papers

    The Method of Alternating Chains

    Semantic Construction of Lewis'S Systems S4 and S5

    Continuous Model Theory

    Independence Results in Set Theory

    Boolean Notions Extended to Higher Dimensions

    Elementary Theories with Models without Automorphisms

    Combinatorial Theorems for the Construction of Models

    Some Applications of the Notions of Forcing and Generic Sets (Summary)

    A Hypothesis Concerning the Extension of Finite Relations and its Verification for Certain Special Cases. First Part

    The Theories of Functors and Models

    Languages with Added Quantifier "There Exist at Least Nα"

    Model-Theoretic Methods in the Study of Elementary Logic

    Extensions of Relational Structures

    Finite Approximations of Infinitely Long Formulas

    Topics in the Theory of Definition

    Logical Structures Arising in Quantum Theory

    Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations

    Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi

    The Fraenkel-Mostowski Method for Independence Proofs in Set Theory

    Free Product in General Algebras

    Model-Theoretic Methods and Results in the Theory of Cylindric Algebras

    Reductions of Higher-Order Logic

    Omitting Classes of Elements

    Universal Groups of Automorphisms of Models

    Topics in Non-Archimedean Mathematics

    The Decision Problem for Fields

    On Models of Elementary Elliptic Geometry

    Logic with Denumerably Long Formulas and Finite Strings of Quantifiers

    Non-Standard Models for Fragments of Number Theory

    Applications of Model Theory to Degrees of Unsolvability

    Logics Appropriate to Empirical Theories

    On the Denumerable Models of Theories with Extra Predicates

    A Löwenheim-Skolem Theorem for Cardinals Far Apart

    Contributed Papers

    Synonymous Theories

    Finite-Quantifier Equivalence

    Algebraic Theories, Algebraic Categories, and Algebraic Functors

    Extensive Ultraproducts and Haar Measure


    Relatively Categorical and Normal Theories

    Free Structures and Categories

    Finite-Dimensional Analogues to Boolean Algebras

    Boolean Recursive Functions and Closure Algebra

    A Unifying Principle in Quantification Theory

    2No can be Anything it Ought to be

    Construction of a Model For Gödel-Bernays Set Theory for which the Class of Natural Numbers is a Set of the Model and a Proper Class in the Theory

    Bibliography with Explanatory Notes

    Some Notes on the Theory Of Models

    A Bibliography of the Theory of Models

    List of Registered Participants

Product details

  • No. of pages: 510
  • Language: English
  • Copyright: © North Holland 1963
  • Published: January 1, 1963
  • Imprint: North Holland
  • eBook ISBN: 9781483275345

About the Editors

J.W. Addison

Leon Henkin

Alfred Tarski

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