Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.
Author(s): Thomas Jech
Series: Springer Monographs in Mathematics
Edition: 3rd
Publisher: Springer
Year: 2006
Language: English
Pages: 787
Cover
......Page 1
Springer Monographs in Mathematics......Page 2
Set Theory: The Third Millennium Edition, revised and expanded......Page 4
3540440852......Page 5
Preface
......Page 8
Contents
......Page 10
Part I - Basic Set Theory
......Page 16
1. Axioms of Set Theory
......Page 18
2. Ordinal Numbers
......Page 32
3. Cardinal Numbers
......Page 42
4. Real Numbers
......Page 52
5. The Axiom of Choice and Cardinal Arithmetic
......Page 62
6. The Axiom of Regularity
......Page 78
7. Filters, Ultrafilters and Boolean Algebras
......Page 88
8. Stationary Sets
......Page 106
9. Combinatorial Set Theory
......Page 122
10. Measurable Cardinals
......Page 140
11. Borel and Analytic Sets
......Page 154
12. Models of Set Theory
......Page 170
Part II - Advanced Set Theory
......Page 188
13. Constructible Sets
......Page 190
14. Forcing
......Page 216
15. Applications of Forcing
......Page 240
16. Iterated Forcing and Martin's Axiom
......Page 282
17. Large Cardinals
......Page 300
18. Large Cardinals and L
......Page 326
19. Iterated Ultrapowers and L[U]
......Page 354
20. Very Large Cardinals
......Page 380
21. Large Cardinals and Forcing
......Page 404
22. Saturated Ideals
......Page 424
23. The Nonstationary Ideal
......Page 456
24. The Singular Cardinal Problem
......Page 472
25. Descriptive Set Theory
......Page 494
26. The Real Line
......Page 526
Part III - Selected Topics
......Page 558
27. Combinatorial Principles in L
......Page 560
28. More Applications of Forcing
......Page 572
29. More Combinatorial Set Theory
......Page 588
30. Complete Boolean Algebras
......Page 600
31. Proper Forcing
......Page 616
32. More Descriptive Set Theory
......Page 630
33. Determinacy
......Page 642
34. Supercompact Cardinals and the Real Line
......Page 663
35. Inner Models for Large Cardinals
......Page 675
36. Forcing and Large Cardinals
......Page 685
37. Martin's Maximum
......Page 697
38. More on Stationary Sets
......Page 711
Bibliography
......Page 723
Notation
......Page 749
Name Index
......Page 759
Index
......Page 765
