Introduction to Set Theory, Third Edition, Revised and Expanded / Edition 3

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Overview

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.

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Editorial Reviews

Mathematical Reviews
...In the third edition, Chapter 11 has been expanded, and four new chapters have been added.
American Mathematical Monthly
...a fine text....The proofs are both elegant and readable.
LEnseignement mathematique
...offers many benefits including...interesting applications of abstract set theory to real analysis...enriching standard classroom material.
Mathematical Intelligencer
...an excellent and much needed book...Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments.
Quarterly Review of Applied Mathematics
The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers.
Mathematica Bohemica
...a very good middle-level set theory text and contains carefully selected material.
Booknews
Revised edition intended as a primary text for mathematics courses. Basic material covered includes: relations, functions, and orderings; finite, countable, and uncountable sets; and cardinal and ordinal numbers. Advanced material discussed includes the Axiom of Choice, filters, ultrafilters, closed unbounded and stationary sets, partitions, large and measurable cardinals, well-founded and non- well-founded sets, partition calculus, and other topics. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Sets; relations, functions and orderings; natural numbers; finite, countable and uncountable sets; cardinal numbers; ordinal numbers; alephs; the axiom of choice; arithmetic of cardinal numbers; sets of real numbers; filters and ultrafilters; combinatorial set theory; large cardinals; the axiom of foundation; the axiomatic set theory.

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    Posted November 4, 2008

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    Posted July 10, 2010

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