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Introduction to Axiomatic Set Theory

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Author(s): Gaisi Takeuti, Wilson M. Zaring
Series: Graduate texts in mathematics1
Edition: 2nd
Publisher: Springer New York
Year: 1982

Language: English
Pages: 260

Front Cover......Page 1
Title Page......Page 4
Preface......Page 6
Preface to Second Edition......Page 8
Contents......Page 10
01 Introduction......Page 12
02 Language and Logic......Page 15
03 Equality......Page 18
04 Classes......Page 21
05 The Elementary Properties of Classes......Page 26
06 Functions and Relations......Page 34
07 Ordinal Numbers......Page 46
08 Ordinal Arithmetic......Page 67
09 Relational Closure and the Rank Function......Page 84
10 The Axiom of Choice and Cardinal Numbers......Page 93
11 Cofinality, the Generalized Continuum Hypothesis, and Cardinal Arithmetic......Page 111
12 Models......Page 122
13 Absoluteness......Page 132
14 The Fundamental Operations......Page 154
15 The Godel Model......Page 164
16 Silver Machines......Page 196
17 Applications of Silver Machines......Page 210
18 Introduction to Forcing......Page 226
19 Forcing......Page 234
Bibliography......Page 240
Problem List......Page 242
Appendix......Page 246
Index of Symbols......Page 248
Index......Page 252
Back Cover......Page 258