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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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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Descrizione libro Springer, 1994. Hardcover. Condizione libro: New. Codice libro della libreria P110387941800
Descrizione libro Springer, 1994. Hardcover. Condizione libro: New. 1. This item is printed on demand. Codice libro della libreria DADAX0387941800