Introduction to Modern Set Theory

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John Wiley & Sons, Jan 16, 1990 - Mathematics - 156 pages
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This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
 

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Contents

Some Mathematical Preliminaries
1
The Axioms Part I
23
Regularity and Choice
49
The Foundation of Mathematics
67
Infinite Nwnbers
73
Two Models of Set Theory
101
Infinite Combinatorics
111
Bibliography
147
Index
153
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Page 147 - THEORY (GENERAL) van Dalen, D., Doets, HC, and de Swart, H., Sets: Naive, Axiomatic and Applied, Pergamon, London, 1978. Henle, J., An Outline of Set Theory, Springer- Verlag, New York, 1986. Jech, T., Set Theory, Academic Press, New York, 1978. FORCING Burgess, J., "Forcing," in Handbook of Mathematical Logic, J.

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