Set Theory and the Continuum Problem - Brossura

Smullyan, Raymond M.; Fitting, Melvin

Brossura

ISBN 10: 0486474844 ISBN 13: 9780486474847

Casa editrice: Dover Pubns, 2010

Riassunto

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.

Su questo libro

L'autore:

Raymond Smullyan received his PhD from Princeton University and taught at Dartmouth, Princeton, Indiana University, and New York's Lehman College. Best known for his mathematical and creative logic puzzles and games, he was also a concert pianist and a magician. He wrote over a dozen books of logic puzzles and texts on mathematical logic.Melvin Fitting, a former student of Dr. Smullyan, is Professor of Mathematics and Computer Science at Lehman College, City University of New York.

Contenuti:

Preface to the Revised 2010 Edition Preface I Axiomatic Set Theory 1. General Background 2. Some Basics of Class-Set Theory 3. The Natural Numbers 4. Superinduction, Well Ordering and Choice 5. Ordinal Numbers 6. Order Isomorphism and Transfinite Recursion 7. Rank 8. Foundation, Induction and Rank 9. Cardinals II Consistency of the Continuum Hypothesis 10. Mostowski-Shepherdson Mappings 11. Reflection Principles 12. Constructible Sets 13. L is a Well-Founded First-Order Universe 14. Constructibility is Absolute Over L 15. Constructibility and the Continuum Hypothesis III Forcing and Independence Results 16. Forcing, the Very Idea 17. The Construction of S 4 Models for ZF 18. The Axiom of Constructibility is Independent 19. Independence in the Continuum Hypothesis 20. Independence of the Axiom of Choice 21. Constructing Classical Models 22. Forcing Backward Bibliography Index List of Notation

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2010
• ISBN 10: 0486474844
• ISBN 13: 9780486474847
• Rilegatura: Copertina flessibile
• Numero di pagine: 315