The Joy of Sets: Fundamentals of Contemporary Set Theory / Edition 2
  • The Joy of Sets: Fundamentals of Contemporary Set Theory / Edition 2
  • The Joy of Sets: Fundamentals of Contemporary Set Theory / Edition 2

The Joy of Sets: Fundamentals of Contemporary Set Theory / Edition 2

by Keith Devlin
     
 

This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for 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

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Overview

This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for 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 from a rigorous answer to the question, "what is a set?" 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 provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel. The author is a well-known mathematician and the editor of the "Computers in Mathematics" column in the AMS Notices and of FOCUS, the magazine published by the MAA.

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Product Details

ISBN-13:
9780387940946
Publisher:
Springer New York
Publication date:
08/03/1993
Series:
Undergraduate Texts in Mathematics Series
Edition description:
2nd ed. 1993. Corr. 2nd printing 1994
Pages:
194
Product dimensions:
0.56(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface; 1. Naïve 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

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