ABSTRACT

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.

chapter 1|16 pages

Sets

chapter 2|22 pages

Relations, Functions, and Orderings

chapter 3|26 pages

Natural Numbers

chapter 4|28 pages

Finite, Countable, and Uncountable Sets

chapter 5|10 pages

Cardinal Numbers

chapter 6|26 pages

Ordinal Numbers

chapter 7|8 pages

chapter 8|18 pages

The Axiom of Choice

chapter 9|15 pages

Arithmetic of Cardinal Numbers

chapter 10|30 pages

Sets of Real Numbers

chapter 11|15 pages

Filters and Ultrafilters

chapter 12|23 pages

Combinatorial Set Theory

chapter 13|10 pages

Large Cardinals

chapter 14|16 pages

The Axiom of Foundation

chapter 15|18 pages

The Axiomatic Set Theory