Notes On Set Theory

Paperback | December 8, 2005

byYiannis Moschovakis

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The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author added solutions to the exercises, and rearranged and reworked the text in several places to improve the presentation.The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy.

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The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory...

Format:PaperbackDimensions:296 pages, 9.25 × 6.1 × 0.27 inPublished:December 8, 2005Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:038728723X

ISBN - 13:9780387287232

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Table of Contents

Introduction * Equinumerosity * Paradoxes and axioms * Are sets all there is? * The natural numbers * Fixed points * Well ordered sets * Choices * Choice's consequences * Baire space * Replacement and other axioms * Ordinal numbers * A. The real numbers * B. Axioms and universes * Index

Editorial Reviews

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 LogicThis 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