Set Theory

by Jech, Thomas J.

• ISBN13: 9780123819505
• ISBN10: 0123819504
• Format: Hardcover
• Copyright: 1978-01-01
• Publisher: Academic Pr

Summary

Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.

Table of Contents

Basic Set Theory

Axioms of Set Theory

Ordinal Numbers

Cardinal Numbers

Real Numbers

The Axiom of Choice and Cardinal Arithmetic

The Axiom of Regularity

Filters, Ultrafilters and Boolean Algebras

Stationary Sets

Combinatorial Set Theory

Measurable Cardinals

Borel and Analytic Sets

Models of Set Theory

Advanced Set Theory

Constructible Sets

Forcing

Applications of Forcing

Iterated Forcing and Martin's Axiom

Large Cardinals

Large Cardinals and L

Iterated Ultrapowers and L++G++U++++

Very Large Cardinals

Large Cardinals and Forcing

Saturated Ideals

The Nonstationary Ideal

The Singular Cardinal Problem

Descriptive Set Theory

The Real Line

Selected Topics

Combinatorial Principles in L

More Applications of Forcing

More Combinatorial Set Theory

Complete Boolean Algebras

Proper Forcing

More Descriptive Set Theory

Determinacy

Supercompact Cardinals and the Real Line

Inner Models for Large Cadinals

Forcing and Large Cardinals

Martin's Maximum

More on Stationary Sets

Bibliography

Notation

Index

Name Index.

Table of Contents provided by Publisher. All Rights Reserved.