Set Theory: The Third Millennium Edition, revised and expandedSpringer Science & Business Media, 21. märts 2006 - 772 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. |
Contents
1 Axioms of Set Theory | 3 |
2 Ordinal Numbers | 16 |
3 Cardinal Numbers | 27 |
4 Real Numbers | 36 |
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 |
743 | |
748 | |
Other editions - View all
Set Theory: The Third Millennium Edition, revised and expanded Thomas Jech No preview available - 2013 |
Common terms and phrases
a₁ antichain assume Axiom of Choice Borel sets canonical closed unbounded set cofinality compact cardinal complete Boolean algebra construct contradiction Corollary defined Definition denote dense disjoint elementary embedding elements equivalence Exercise exists extension filter finite follows formula function f hence ideal implies inaccessible cardinal indiscernibles induction infinite inner model isomorphic iterated ultrapowers large cardinals Lebesgue measurable Lemma Let F let ƒ Let G limit ordinal Math meager measurable cardinal model of ZFC nonempty nonprincipal normal measure notion of forcing one-to-one order-type partially ordered partition proof of Theorem prove regular cardinal semiproper sequence set of reals set theory Shelah singular cardinal Skolem Solovay stationary set stationary subset subalgebra subset of ê supercompact Suslin tree transitive model ultrafilter ultrapower w₁ weakly compact well-founded well-ordering winning strategy Woodin cardinal