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

Moschovakis, Yiannis

Hardcover

ISBN 10: 0387941800 ISBN 13: 9780387941806

Publisher: Springer, 1994

Synopsis

The book 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 faithful representation of mathematical objects by structured sets.

About this title

Review

The text is engaging, lively, and sophisticated; the historical development makes it especially attractive...the book is a gem, densely packed with fantastic problems, and clear, elegant proofs. -- Joel David Hamkins, Journal of Symbolic Logic, December 1997

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 0387941800
• ISBN 13: 9780387941806
• Binding: Hardcover
• Edition number: 1
• Number of pages: 292