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

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

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.

### What people are saying -Write a review

#### 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 Copyright

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