Preface.

1: The Axiom of Extension.

2: The Axiom of Specification.

3: Unordered Pairs.

4: Unions and Intersections.

5: Complements and Powers.

6: Ordered Pairs.

7: Relations.

8: Functions.

9: Families.

10: Inverses and Composites.

11: Numbers.

12: The Peano Axioms.

13: Arithmetic.

14: Order.

15: The Axiom of Choice.

16: Zorn's Lemma.

17: Well Ordering.

18: Transfinite Recursion.

19: Ordinal Numbers.

20: Sets of Ordinal Numbers.

21: Ordinal Arithmetic.

22: The Schröder-Bernstein Theorem.

23: Countable Sets.

24: Cardinal Arithmetic.

25: Cardinal numbers.

Index

This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in twenty-five brief chapters.
"This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' ... who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. ... A good reference for how set theory is used in other parts of mathematics."?Allen Stenger, The Mathematical Association of America, September 2011.
Dover (2017) republication of the edition originally published by D. Van Nostrand Co., Princeton, New Jersey, 1960.
www.doverpublications.com

Hungarian-born Paul R. Halmos (1916?2006) is widely regarded as a top-notch expositor of mathematics. He taught at the University of Chicago and the University of Michigan as well as other universities and made significant contributions to several areas of mathematics including mathematical logic, probability theory, ergodic theory, and functional analysis.