The Joy of Sets Fundamentals of Contemporary Set Theory~tqw~ darksiderg
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Comments:*******************************************************************************<br /> The Joy of Sets: Fundamentals of Contemporary Set Theory<br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 11,072,905 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> This book provides an account of those parts of contemporary set theory that are <br /> relevant to other areas of pure mathematics. Intended for advanced <br /> undergraduates and beginning graduate students, the text is written in an easy-<br /> going style, with a minimum of formalism. The book begins with a review of <br /> "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, <br /> showing how they arise naturally from a rigorous answer to the question, "what <br /> is a set?" After discussing the ordinal and cardinal numbers, the book then <br /> delves into contemporary set theory, covering such topics as: the Borel <br /> hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two <br /> chapters present an extension of the Zermelo-Fraenkel theory, discussing the <br /> axiom of constructibility and the question of provability in set theory. A final <br /> chapter presents an account of an alternative conception of set theory that has <br /> proved useful in computer science, the non-well-founded set theory of Peter <br /> Aczel. The author is a well-known mathematician and the editor of the "Computers <br /> in Mathematics" column in the AMS Notices and of FOCUS, the magazine published <br /> by the MAA.<br /> <br /> Table of Contents<br /> <br /> Preface <br /> 1 Naive Set Theory 1<br /> 2 The Zermelo-Fraenkel Axioms 29<br /> 3 Ordinal and Cardinal Numbers 66<br /> 4 Topics in Pure Set Theory 101<br /> 5 The Axiom of Constructibility 120<br /> 6 Independence Proofs in Set Theory 130<br /> 7 Non-Well-Founded Set Theory 143<br /> Bibliography 185<br /> Glossary of Symbols 185<br /> Index 189<br /> <br /> Product Details<br /> <br /> * ISBN: 0387940944<br /> * ISBN-13: 9780387940946<br /> * Format: Textbook Hardcover, 212pp<br /> * Publisher: Springer-Verlag New York, LLC<br /> * Pub. Date: June 1994<br /> * Edition Number: 2<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader<br /> <br />
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