The joy of sets : fundamentals of contemporary set theory
著者
書誌事項
The joy of sets : fundamentals of contemporary set theory
（Undergraduate texts in mathematics）
Springer-Verlag, c1993
2nd ed
- : gw
- : us
- タイトル別名
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Fundamentals of contemporary set theory
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注記
Rev. ed. of: Fundamentals of contemporary set theory. c1979
Includes bibliographical references (p. 185) and index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387940946
内容説明
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.
目次
- 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
- 巻冊次
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: gw ISBN 9783540940944
内容説明
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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