Title
Set Theory and the Continuum Problem (Dover Books on Mathematics),New
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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 MostowskiShepherdson mappings, reflection principles, constructible sets and constructibility, and the continuum hypothesis. The text concludes with a sevenchapter 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.
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We provide a 2-year limited warranty, from the date of purchase for all our products.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Set Theory and the Continuum Problem'? A: The book primarily focuses on axiomatic set theory, exploring the consistency of the continuum hypothesis, and examining forcing and independence results.
- Q: Who is the author of this book? A: The author of 'Set Theory and the Continuum Problem' is Raymond M. Smullyan.
- Q: How many pages does the book contain? A: The book contains a total of 336 pages.
- Q: What type of binding does this book have? A: This edition of the book is available in paperback binding.
- Q: When was 'Set Theory and the Continuum Problem' published? A: The book was published on April 21, 2010.
- Q: What topics are covered in the first part of the book? A: The first part covers axiomatic set theory, including topics like size comparisons between infinite sets, double induction principle, ordinal numbers, and transfinite recursion.
- Q: Is this book suitable for graduate students? A: Yes, the book is designed to be accessible and understandable for graduate students of mathematics.
- Q: What is the significance of the continuum hypothesis in this book? A: The continuum hypothesis is explored in detail in the second part, addressing its consistency and related mathematical principles.
- Q: Are there any special features in the book? A: The book is noted for its clear explanations of technical proofs and its engaging discussions on countability and uncountability.
- Q: What edition of the book is this? A: This is the revised edition of 'Set Theory and the Continuum Problem'.