Cantorian Set Theory and Limitation of Size

by Michael Hallett

Overview

Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.

Product Details

ISBN-13:	9780198532835
Publisher:	Oxford University Press
Publication date:	12/18/1986
Series:	Oxford Logic Guides , #10
Edition description:	REPRINT
Pages:	343
Product dimensions:	9.16(w) x 6.20(h) x 0.79(d)

About the Author

McGill University, Montreal

Table of Contents

Foreword by Professor Michael Dummett
Preface
Part I The Cantorian Origins of Set Theory
Introduction to Part I: The Background to the Theory of Ordinals
1. Cantor's Theory of Infinity
2. The Ordinal Theory of Powers
3. Cantor's Theory of Number
4. The Origin of the Limitation of Size Idea
Part 2 The Limitation of Size Argument and Axiomatic Set Theory
Introduction to Part 2
5. The Limitation of Size Argument
6. The Completability of Sets
7. The Zermelo System
8. Von Neumann's Reinstatement of the Ordinal Theory of Size
Conclusion

Editorial Reviews

"Here is the first full-length study to do justice both to the mathematical importance of Cantor's work and to the philosophical ideas that governed it....The book is very well informed mathematically, yet much of Hallett's perceptive comment on and his patient and sympathetic interpretation of the philosophical ideas of Cantor and the other founders of set theory will be readily intelligible to nonspecialists, making the book of great interest to mathematician and philosopher alike."—Choice

"Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics."—The American Mathematical Monthly

From the Publisher