Set Theory: The Third Millennium Edition, revised and expandedSpringer Science & Business Media, 21 de març 2006 - 772 pàgines 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. |
Continguts
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 | |
Altres edicions - Mostra-ho tot
Set Theory: The Third Millennium Edition, revised and expanded Thomas Jech Previsualització limitada - 2007 |
Set Theory: The Third Millennium Edition, revised and expanded Thomas Jech Previsualització no disponible - 2013 |
Frases i termes més freqüents
assume Axiom Baire Boolean algebra Borel bounded called canonical Chapter Choice Clearly cofinal collapse collection compact complete condition consider consistency constant construct contains contradiction Corollary countable define defined Definition denote dense direct disjoint elementary embedding elements equivalence Exercise exists extension fact filter find finite follows forcing formula function f given hence holds ideal implies inaccessible induction infinite isomorphic iteration least Lemma length limit ordinal mapping maximal measurable cardinal nonempty normal measure Note partition perfect plays Proof proof of Theorem prove reals regular cardinal relation result satisfies sequence set theory singular stationary set strategy strong subset Theorem transitive model tree ultrafilter ultrapower uncountable union unique weakly well-founded well-ordering winning Woodin