Set Theory: The Third Millennium Edition, Revised and Expanded

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Springer Science & Business Media, 2003 - Mathematics - 769 pages
1 Review

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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Review: Set Theory: The Third Millennium Edition, Revised and Expanded

User Review  - Michael Hoffman - Goodreads

Just started reading this, I am actually surprised at the clarity of it so far. Most math books of this size tend to try and do too much and lose the forest for the trees. Read full review

Review: Set Theory: The Third Millennium Edition, Revised and Expanded

User Review  - Tony Strimple - Goodreads

Stellar coverage of the fundamentals of set theory, albeit a bit verbose. Kunen's succinct treatment, however, is still better overall. Good for a quiet weekend. I'll let you know how the sections on large cardinals pan out. Read full review

Contents

1 Axioms of Set Theory
3
2 Ordinal Numbers
16
3 Cardinal Numbers
27
4 Real Numbers
37
5 The Axiom of Choice and Cardinal Arithmetic
46
6 The Axiom of Regularity
63
7 Filters Ultrafilters and Boolean Algebras
72
8 Stationary Sets
91
23 The Nonstationary Ideal
440
24 The Singular Cardinal Problem
457
25 Descriptive Set Theory
479
26 The Real Line
510
Selected Topics
542
27 Combinatorial Principles in L
543
28 More Applications of Forcing
557
29 More Combinatorial Set Theory
573

9 Combinatorial Set Theory
106
10 Measurable Cardinals
125
11 Borel and Analytic Sets
139
12 Models of Set Theory
154
Advanced Set Theory
173
13 Constructible Sets
175
14 Forcing
201
15 Applications of Forcing
225
16 Iterated Forcing and Martins Axiom
266
17 Large Cardinals
285
18 Large Cardinals and L
310
19 Iterated Ultrapowers and LU
339
20 Very Large Cardinals
365
21 Large Cardinals and Forcing
388
22 Saturated Ideals
409
30 Complete Boolean Algebras
584
31 Proper Forcing
601
32 More Descriptive Set Theory
615
33 Determinacy
627
34 Supercompact Cardinals and the Real Line
646
35 Inner Models for Large Cardinals
659
36 Forcing and Large Cardinals
669
37 Martins Maximum
681
38 More on Stationary Sets
695
Bibliography
707
Notation
733
Name Index
743
Index
748
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