Book:Thomas Jech/Set Theory/Second Edition

Subject Matter

 * Set Theory

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&mdash;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 $\Sigma_n$ 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 APPLICATINOS 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 Indiscernibles
 * 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. $\Sigma^1_n$ and $\Pi^1_n$ 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
 * Name Index
 * List of Corrections