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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
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Notes on Set Theory (Undergraduate Texts in Mathematics)
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Notes on Set Theory
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Notes on set theory. Undergraduate texts in mathematics.
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New York, Springer [1994]., 1994
ISBN 10: 0387941800
ISBN 13: 9780387941806
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Hardcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 04 MOS 9780387941806 Sprache: Englisch Gewicht in Gramm: 1150. Seller Inventory # 2504380
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Notes on Set Theory (Undergraduate Texts in Mtahematics)
Published by
Springer-Verlag, New York, 1994
ISBN 10: 0387941800
ISBN 13: 9780387941806
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Notes on Set Theory
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Condition: Gut. Zustand: Gut | Seiten: 272 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 1402475/3
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