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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:
Introduction to Modern Set Theory (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Synopses & Reviews
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.
Table of Contents
Some Mathematical Preliminaries.
Partially Ordered Sets.
Some Facts About Partially Ordered Sets.
THE AXIOMS, PART I. The Language, Some Finite Operations, and Extensionality.
Union, Intersection, and Separation.
Filters and Ideas.
The Natural Numbers.
Two Nonconstructive Axioms: Infinity and Power Set.
A Digression on the Power Set Axiom.
REGULARITY AND CHOICE.
A First Look at Ordinals.
A World About Classes.
The Axiom of Choice.
Four Forms of the Axiom of Choice.
Models of Regularity and Choice.
THE FOUNDATION OF MATHEMATICS.
Infinite Operations and More Exponentiation.
TWO MODELS OF SET THEORY.
A Set Model for ZFC.
The Constructible Universe.
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