The joy of sets : fundamentals of contemporary set theory
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Bibliographic Information
The joy of sets : fundamentals of contemporary set theory
（Undergraduate texts in mathematics）
Springer-Verlag, c1993
2nd ed
- : gw
- : us
- Other Title
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Fundamentals of contemporary set theory
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Note
Rev. ed. of: Fundamentals of contemporary set theory. c1979
Includes bibliographical references (p. 185) and index
Description and Table of Contents
- Volume
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: us ISBN 9780387940946
Description
This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naive" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.
Table of Contents
- Preface
- 1. Naive Set Theory
- 2. The Zermelo-Fraenkel Axioms
- 3. Ordinal and Cardinal Numbers
- 4. Topics in Pure Set Theory
- 5. The Axiom of Constructibility
- 6. Independence Proofs in Set Theory
- 7. Non-Well-Founded Set Theory
- Bibliography
- Glossary of Symbols
- Index
- Volume
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: gw ISBN 9783540940944
Description
This treatise is intended to provide an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Aimed at advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory. It then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally. After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of probability in set theory. A final chapter presents an account of an alternative concept of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel.
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