| Set Theory and the Continuum Problem Contributor(s): Smullyan, Raymond M. (Author), Fitting, Melvin (Author) |
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ISBN: 0486474844 ISBN-13: 9780486474847 Publisher: Dover Publications OUR PRICE: $14.36 Product Type: Paperback Published: May 2010 Annotation: Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms, development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's proofs of the independence of the continuum hypothesis and the axiom of choice. It also presents, for the first time in a textbook, the double induction and superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory. |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory |
| Dewey: 511.322 |
| LCCN: 2009036172 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.8" H x 5.9" W x 8.9" (0.85 lbs) 336 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: A lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis, and the final section examines forcing and independence results. Part One's focus on axiomatic set theory features nine chapters that examine problems related to size comparisons between infinite sets, basics of class theory, and natural numbers. Additional topics include author Raymond Smullyan's double induction principle, super induction, ordinal numbers, order isomorphism and transfinite recursion, and the axiom of foundation and cardinals. The six chapters of Part Two address Mostowski-Shepherdson mappings, reflection principles, constructible sets and constructibility, and the continuum hypothesis. The text concludes with a seven-chapter exploration of forcing and independence results. This treatment is noteworthy for its clear explanations of highly technical proofs and its discussions of countability, uncountability, and mathematical induction, which are simultaneously charming for experts and understandable to graduate students of mathematics. |