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Introduction to axiomatic set theory

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In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an  Read more...

Abstract:
In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con- sistency of the Axiom of Choice (AC) and the  Read more...

Author(s): Zaring, Wilson M.; Takeuti, Gaisi
Series: Graduate texts in mathematics 1
Edition: 2nd ed
Publisher: Springer-Verlag
Year: 1982

Language: English
Pages: 246
City: New York
Tags: Axiomatic set theory.;Axiomatik;Mengenlehre;Mathematics.;Mathematical Logic and Foundations.

Content: 1 Introduction --
2 Language and Logic --
3 Equality --
4 Classes --
5 The Elementary Properties of Classes --
6 Functions and Relations --
7 Ordinal Numbers --
8 Ordinal Arithmetic --
9 Relational Closure and the Rank Function --
10 The Axiom of Choice and Cardinal Numbers --
11 Cofinality, the Generalized Continuum Hypothesis, and Cardinal Arithmetic --
12 Models --
13 Absoluteness --
14 The Fundamental Operations --
15 The Gödel Model --
16 Silver Machines --
17 Applications of Silver Machines --
18 Introduction to Forcing --
19 Forcing --
Problem List --
Index of Symbols.