Notes on Set Theory (Undergraduate Texts in Mathematics) - Softcover

Moschovakis, Yiannis N.

Softcover

ISBN 10: 3540941800 ISBN 13: 9783540941804

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

This text covers the basic facts about abstract sets, including the axiom of choice, transfinite recursion, cardinals, ordinals and the cumulative hierarchy of well founded sets. It also includes a chapter on Baire space, focusing on results of interest to analysts and introducing the reader to the continuum problem; an appendix with a reasonably detailed construction of the real numbers; and a second appendix introducing set universes, which satisfy conditions that include Aczel's Antifoundation. Most of the results are derived within Zermelo-Fraenkel set theory with depended choices, which allows atoms and non-well founded sets, with the full axiom of choice and the axiom of foundation assumed explicitly where needed. To clarify the role of set theory as a foundation of mathematics - including computation theory - the book uses the notion of the faithful representation of mathematical objects by structured sets.

About this title

Review

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

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1994
• ISBN 10: 3540941800
• ISBN 13: 9783540941804
• Binding: Paperback
• Language: English
• Number of pages: 286