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NOTES ON SET THEORYPDF|Epub|txt|kindle电子书版本网盘下载
- N.MOSCHOVAKIS 著
- 出版社： Springer-Verlag
- ISBN：0387941800
- 出版时间：未知
- 标注页数：272页
- 文件大小：9MB
- 文件页数：283页
- 主题词：
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图书目录
1.Introduction1
Problems for Chapter 15
2.Equinumerosity7
Countable unions of countable sets9
The reals are uncountable11
A ＜c P（A）15
Schroder-Bernstein Theorem16
Problems for Chapter 218
3.Paradoxes and axioms19
The Russell paradox21
Axioms （Ⅰ） - （Ⅱ）24
Axioms for definite conditions and operations27
Classes28
Problems for Chapter 331
4.Are sets all there is？33
Ordered pairs35
Disjoint union36
Relations37
Equivalence relations38
Functions39
Cardinal numbers43
Structured sets45
Problems for Chapter 446
5.The natural numbers53
Existence of the Natural Numbers54
Uniqueness of the Natural Numbers54
Recursion Theorem55
Addition and multiplication59
Pigeonhole Principle64
Strings67
The continuum69
Problems for Chapter 569
6.Fixed points73
Posets73
Partial functions76
Inductive posets77
Continuous Least Fixed Point Theorem79
About topology81
Graphs85
Problems for Chapter 686
Streams87
Scott topology91
Directed-complete posets91
7.Well ordered sets93
Transfinite induction98
Transfinite recursion100
Iteration Lemma100
Comparability of well ordered sets104
Wellfoundedness of ≤0105
Hartogs’ Theorem106
Fixed Point Theorem108
Least Fixed Point Theorem108
Problems for Chapter 7110
8.Choices117
Axiom of Choice117
Equivalents of AC120
Countable Principle of Choice， ACN122
Axiom （Ⅵ） of Dependent Choices， DC122
The axiomatic theories ZDC， ZAC125
Consistency and independence results126
Problems for Chapter 8127
9.Choice’s consequences131
Trees132
Konig’s Lemma133
Fan Theorem134
Wellfoundedness of ＜c134
Best wellorderings135
Absorption laws138
Konig’s Theorem140
Coninality，regular cardinals141
Problems for Chapter 9142
10.Baire space147
Cardinality of perfect pointsets150
Cantor-Bendixson Theorem151
Property P152
Analytic pointsets153
Perfect Set Theorem157
Borel sets160
Counterexample to the general property P162
Consistency and independence results164
Problems for Chapter 10165
Borelisomorphisms166
11.Replacement and other axioms169
Replacement Axiom （Ⅷ）170
The axiomatic theories ZFDC， ZFAC170
Grounded Recursion Theorem172
Transitive classes174
Basic Closure Lemma175
Hereditarily176
nite sets176
Zermelo universes177
The least Zermelo universe179
Grounded sets180
Principle of Foundation180
The axiomatic theory Zermelo-F raenkel， ZFC181
Z-F universes183
von Neumann’s class V183
Mostowski Collapsing Lemma183
Consistency and independence results184
Problems for Chapter 11185
12.Ordinal numbers189
Characterization of the ordinal assignment193
Characterization of the ordinals194
Ordinal recursion197
Ordinal addition， multiplication197
von Neumann cardinals198
The operation ？200
The cumulative rank hierarchy201
Problems for Chapter 12203
The operation ？α205
Strongly inaccessible cardinals206
Frege cardinals206
Quotients of equivalence conditions207
A.The real numbers209
Congruences209
Fields211
Ordered Fields212
Uniqueness of the rationals214
Existence of the rationale215
Countable， dense， linear orderings219
The archimedean property221
Nested interval property226
Dedekind cuts229
Existence of the real numbers231
Uniqueness of the real numbers234
Problems for Appendix A236
B.Axioms and universes239
Set universes242
Propositions and relativizations243
Rieger universes248
Rieger’s Theorem248
Antifoundation Principle， AFA254
Bisimulations255
The antifounded universe259
Aczel’s Theorem259
Problems for Appendix B262
Index267