The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics)

Devlin, Keith

ISBN 10: 0387940944 / ISBN 13: 9780387940946

Editore: Springer, 1993

The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. Codice articolo GOR007045578

Riassunto:

This book is intended to provide 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.

Contenuti: 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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Titolo: The Joy of Sets: Fundamentals of ...
Casa editrice: Springer
Data di pubblicazione: 1993
Legatura: Hardback
Condizione: Very Good
Edizione: seconda edizione