## Set Theory: The Third Millennium Edition, Revised and ExpandedSet 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 - GoodreadsJust 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 - Michael Hoffman - GoodreadsJust 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

### 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 |

707 | |

Notation | 733 |

743 | |

748 | |