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The Joy of Sets Fundamentals of Contemporary Set Theory~tqw~ darksiderg

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The Joy of Sets Fundamentals of Contemporary Set Theory~tqw~ darksiderg

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Name:The Joy of Sets Fundamentals of Contemporary Set Theory~tqw~ darksiderg

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The Joy of Sets: Fundamentals of Contemporary Set Theory
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Type.................: Ebook
Part Size............: 11,072,905 bytes




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Posted by............: ~tqw~

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Release Notes
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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.

Table of Contents

Preface
1 Naive Set Theory 1
2 The Zermelo-Fraenkel Axioms 29
3 Ordinal and Cardinal Numbers 66
4 Topics in Pure Set Theory 101
5 The Axiom of Constructibility 120
6 Independence Proofs in Set Theory 130
7 Non-Well-Founded Set Theory 143
Bibliography 185
Glossary of Symbols 185
Index 189

Product Details

* ISBN: 0387940944
* ISBN-13: 9780387940946
* Format: Textbook Hardcover, 212pp
* Publisher: Springer-Verlag New York, LLC
* Pub. Date: June 1994
* Edition Number: 2

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