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.
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.
"The book remains an excellent text for a senior undergraduate or first-year graduate level course. There is sufficient material for instructors of widely differing views to assemble one-semester courses. . ..the chapter on the axiom of choice is particularly strong. "
". . .a fine text. . ..The proofs are both elegant and readable. "
---American Mathematical Monthly
". . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material. "
". . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments. "
---The Mathematical Intelligencer
"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. "
---Quarterly Review of Applied Mathematics
". . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added. "