Introduction to Axiomatic Set Theory

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...

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Main Authors: Takeuti, G., Zaring, W.M. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 1982, 1982
Edition:2nd ed. 1982
Series:Graduate Texts in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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