Set theory, Volume 79

Thomas Jech9780123819505, 0-12-381950-4, 3-540-44085-2

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.

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Table of contents :
Set Theory……Page 1
Table of Contens……Page 7
Part I – Basic Set Theory……Page 12
01. Axioms of Set Theory……Page 13
02. Ordinal Numbers……Page 26
03. Cardinal numbers……Page 36
04. Real Numbers……Page 45
05. The Axiom of Choice and Cardinal Arithmetic……Page 54
06. The Axiom of Regularity……Page 69
07. Filters, Ultrafilters and Boolean Algebras……Page 78
08. Stationary Sets……Page 95
09. Combinatorial Set Theory……Page 110
10. Measurable Cardinals……Page 127
11. Borel and Analytic Sets……Page 141
12. Models of Set Theory……Page 156
Part II – Advanced Set Theory……Page 174
13. Constructible Sets……Page 175
14. Forcing……Page 201
15. Applications of Forcing……Page 225
16. Iterated Forcing and Marin’s Axiom……Page 266
17. Large Cardinals……Page 283
18. Large Cardinals and L……Page 308
19. Iterated Ultrapowers and L[U]……Page 335
20. Very Large Cardinals……Page 361
21. Large Cardinals and Forcing……Page 384
22. Saturated Ideals……Page 403
23. The Nonstationary Ideal……Page 434
24. The Singular Cardinal Problem……Page 450
25. Descriptive Set Theory……Page 471
26. The Real Line……Page 502
Part III – Selected Topics……Page 533
27. Combinatorial Principles in L……Page 534
28. More Applications of Forcing……Page 546
29. More Combinatorial Set Theory……Page 561
30. Complete Boolean Algebras……Page 572
31. Proper Forcing……Page 587
32. More Descriptive Set Theory……Page 601
33. Determinacy……Page 613
34. Suprcompact Cardinals and the Real Line……Page 632
35. Inner Models for Large Cardinals……Page 644
36. Forcing and Large Cardinals……Page 654
37. Martin’s Maximum……Page 666
38. More on Stationary Sets……Page 680
Bibliogaphy……Page 691
Notation……Page 717
Name Index……Page 727
Index……Page 732