Items related to Notes on Set Theory (Undergraduate Texts in Mathematics)
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.
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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
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date1994
- ISBN 10 0387941800
- ISBN 13 9780387941806
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages292
- Rating
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Hardcover. Condition: Fine. 24.5 x 16 cm. xiv 272pp. Bound into glossy yellow boards. Undergraduate Texts in Mathematics. Seller Inventory # 79340
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Notes on Set Theory (Undergraduate Texts in Mtahematics)
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Springer-Verlag, New York, 1994
ISBN 10: 0387941800
ISBN 13: 9780387941806
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