The Theory of Models - 1st Edition - ISBN: 9780720422337, 9781483275345

The Theory of Models

1st Edition

Proceedings of the 1963 International Symposium at Berkeley

Editors: J.W. Addison Leon Henkin Alfred Tarski
eBook ISBN: 9781483275345
Imprint: North Holland
Published Date: 1st January 1963
Page Count: 510
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Description

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

Preface

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

Abstracts

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

Details

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

About the Editor

J.W. Addison

Leon Henkin

Alfred Tarski