Notes on Set Theory - Rilegato

Moschovakis, Yiannis N

Rilegato

ISBN 10: 0387941800 ISBN 13: 9780387941806

Casa editrice: Springer-Verlag New York Inc., 1994

Riassunto

What this book is about. The theory of sets is a vibrant, exciting math­ ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun­ dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab­ stract sets," including the Axiom of Choice, transfinite recursion, and car­ dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

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Recensione

About the First Edition:

This is a sophisticated undergraduate set theory text, brimming with mathematics, and packed with elegant proofs, historical explanations, and enlightening exercises, all presented at just the right level for a first course in set theory.
- Joel David Hamkins, Journal of Symbolic Logic

This is an excellent introduction to axiomatic set theory, viewed both as a foundation of mathematics and as a branch of mathematics with its own subject matter, basic results, open problems.
- Achille C. Varzi, History and Philosophy of Logic

From the reviews of the second edition:

"The author of this very nice introduction into the basic facts of set theory has, in this second edition modified his presentation ... simplified proofs, and streamlined the terminology and notation. All the advantages of this text remained." (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1088 (14), 2006)

Product Description

Book by Moschovakis Yiannis

Dettagli dell?edizione

• Editore: Springer-Verlag New York Inc.
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 0387941800
• ISBN 13: 9780387941806
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 292
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com