Book contents
- Frontmatter
- Contents
- Preface
- Part I Introduction to set theory
- Introduction
- 1 Notation, conventions
- 2 Definition of equivalence. The concept of cardinality. The Axiom of Choice
- 3 Countable cardinal, continuum cardinal
- 4 Comparison of cardinals
- 5 Operations with sets and cardinals
- 6 Examples
- 7 Ordered Sets. Order Types. Ordinals
- 8 Properties of wellordered sets. Good sets. The ordinal operation
- 9 Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem
- 10 Definition of the cardinality operation. Properties of cardinalities. The cofinality operation
- 11 Properties of the power operation
- Hints for solving problems marked with * in Part I
- Appendix. An axiomatic development of set theory
- Part II Topics in combinatorial set theory
- Bibliography
- List of symbols
- Name index
- Subject index
4 - Comparison of cardinals
Published online by Cambridge University Press: 10 May 2010
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Book contents
- Frontmatter
- Contents
- Preface
- Part I Introduction to set theory
- Introduction
- 1 Notation, conventions
- 2 Definition of equivalence. The concept of cardinality. The Axiom of Choice
- 3 Countable cardinal, continuum cardinal
- 4 Comparison of cardinals
- 5 Operations with sets and cardinals
- 6 Examples
- 7 Ordered Sets. Order Types. Ordinals
- 8 Properties of wellordered sets. Good sets. The ordinal operation
- 9 Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem
- 10 Definition of the cardinality operation. Properties of cardinalities. The cofinality operation
- 11 Properties of the power operation
- Hints for solving problems marked with * in Part I
- Appendix. An axiomatic development of set theory
- Part II Topics in combinatorial set theory
- Bibliography
- List of symbols
- Name index
- Subject index
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- Set Theory , pp. 21 - 27Publisher: Cambridge University PressPrint publication year: 1999