Set Theory and Its Logic

by Quine, W. V.

• ISBN13: 9780674802070
• ISBN10: 0674802071
• Edition: Revised
• Format: Paperback
• Copyright: 2000-05-05
• Publisher: Belknap Pr

Summary

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

Table of Contents

Introduction

The Elements

Logic Quantification and identity Virtual Classes Virtual relations

Real Classes Reality, extensionality, and The individual The virtual Amid The real Identity and substitution

Classes of Classes Unit Classes Unions, intersections, descriptions Relations As Classes of pairs Functions

Natural Numbers Numbers unconstrued Numbers construed Induction

Iteration and Arithmetic Sequences and iterates The Ancestral Sum, product, power

Higher Forms of Number

Real Numbers Program.

Numerical pairs Ratios and reals construed Existential needs.

Operations and extensions

Order and Ordinals Transfinite induction

Order Ordinal numbers Laws of ordinals

The order of The ordinals

Transfinite Recursion

Transfinite recursion Laws of Transfinite recursion Enumeration

Cardinal Numbers Comparative size of Classes

The SchrOder-Bernstein

Theorem Infinite cardinal numbers

The Axiom of Choice Selections and selectors

Further equivalents of The Axiom

The place of The Axiom

Axiom Systems

Russell'S Theory of Types

The constructive part Classes and The Axiom of reducibility

The modern Theory of types

General Variables and Zermelo

The Theory of types with general variables

Cumulative types and Zermelo Axioms of infinity and Others

Stratification and Ultimate Classes "New foundations" Non-Cantorian Classes.

Induction Again Ultimate Classes Added

Von Neumann'S System and Others

The von Neumann-Bernays system Departures and comparisons Strength of systems

Synopsis of Five Axiom Systems List of Numbered Formulas

Bibliographical

References

Index

Table of Contents provided by Publisher. All Rights Reserved.