# Book:Thomas Jech/Set Theory/Second Edition

## Thomas Jech: Set Theory (2nd Edition)

Published $1997$, Springer Verlag

ISBN 3-540-63048-1.

### 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 $\Sigma_n$ 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