Set Theory and the Continuum Problem
World of Books
The feel-good place to buy books
Set Theory and the Continuum Problem by Martin Davis
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.
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.
Fitting, Melvin: - Melvin Fitting is Professor Emeritus at the City University of New York. He has written or edited a dozen books, and has worked in intensional logic, semantics for logic programming, theory of truth, and tableau systems for non-classical logics. In 2012 he received the Herbrand Award from the Conference on Automated Deduction. He was on the faculty of the City University of New York from 1969 to his retirement in 2013, at Lehman College, and at the Graduate Center, where he was in the Departments of Mathematics, Computer Science, and Philosophy.
| SKU | Unavailable |
| ISBN 13 | 9780486474847 |
| ISBN 10 | 0486474844 |
| Title | Set Theory and the Continuum Problem |
| Author | Martin Davis |
| Series | Dover Books On Mathema 14tics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Dover Publications Inc. |
| Year published | 2010-05-28 |
| Number of pages | 336 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |