Set Theory
Academic Press
Published on 23. November 1978
620 pages
978-0-08-087395-4 (ISBN)
Description
Set Theory
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Content
- Front Cover
- Set Theory
- Copyright Page
- Contents
- Preface
- Part I: Sets
- Chapter 1. Axiomatic Set Theory
- 1. Axioms of Set Theory
- 2. Ordinal Numbers
- 3. Cardinal Numbers
- 4. Real Numbers
- 5. The Axiom of Choice
- 6. Cardinal Arithmetic
- 7. Filters and Ideals. Closed Unbounded Sets
- 8. Singular Cardinals
- 9. The Axiom of Regularity
- Appendix: Bernays-Gödel Axiomatic Set Theory
- Chapter 2. Transitive Models of Set Theory
- 10. Models of Set Theory
- 11. Transitive Models of ZF
- 12. Constructible Sets
- 13. Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
- 14. The Sn Hierarchy of Classes, Relations, and Functions
- 15. Relative Constructibility and Ordinal Definability
- Part II: More Sets
- Chapter 3. Forcing and Generic Models
- 16. Generic Models
- 17. Complete Boolean Algebras
- 18. Forcing and Boolean-Valued Models
- 19. Independence of the Continuum Hypothesis and the Axiom of Choice
- 20. More Generic Models
- 21. Symmetric Submodels of Generic Models
- Chapter 4. Some Applications of Forcing
- 22. Suslin's Problem
- 23. Martin's Axiom and Iterated Forcing
- 24. Some Combinatorial Problems
- 25. Forcing and Complete Boolean Algebras
- 26. More Applications of Forcing
- Part III: Large Sets
- Chapter 5. Measurable Cardinals
- 27. The Measure Problem
- 28. Ultrapowers and Elementary Embeddings
- 29. Infinitary Combinatorics
- 30. Silver lndiscernibles
- 31. The Model L[U]
- 32. Large Cardinals below a Measurable Cardinal
- Chapter 6. Other Large Cardinals
- 33. Compact Cardinals
- 34. Real-Valued Measurable Cardinals
- 35. Saturation of Ideals and Generic Ultrapowers
- 36. Measurable Cardinals and the Generalized Continuum Hypothesis
- 37. Some Applications of Forcing in the Theory of Large Cardinals
- 38. More on Ultrafilters
- Part IV: Sets of Reals
- Chapter 7. Descriptive Set Theory
- 39. Borel and Analytic Sets
- 40. S1/n and ?1/n: Sets and Relations in the Baire Space
- 41. Projective Sets in the Constructible Universe
- 42. A Model Where All Sets Are Lebesgue Measurable
- 43. The Axiom of Determinacy
- 44. Some Applications of Forcing in Descriptive Set Theory
- Historical Notes and Guide to The Bibliography
- Bibliography
- Notation
- Index
- Pure and Applied Mathematics
