Peter Komjath, Vilmos Totik Springer, Hardcover, Published May 2006, 514 pages, ISBN 038730293X
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This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Table of Contents

Foreword
Problems: Operations on sets
Countability
Equivalence
Continuum
Sets of reals and real functions
Ordered sets
Order types
Ordinals
Ordinal arithmetic
Cardinals
Partially ordered sets
Transfinite enumeration
Euclidean spaces
Zorn's lemma
Hamel bases
The continuum hypothesis
Ultrafilters on w
Families of sets
The Banach-Tarski paradox
Stationary sets in w1
Stationary sets in larger cardinals
Canonical functions
Infinite graphs
Partition relations
\triangle systems
Set mappings
Trees
The measure problem
Stationary sets
The axiom of choice
Well founded sets and the axiom of foundation
Solutions: Operations on sets
Countability
Equivalence
Continuum
Sets of reals and real functions
Ordered sets
Order types
Ordinals
Ordinal arithmetic
Cardinals
Partially ordered sets
Transfinite enumeration
Euclidean spaces
Zorn's lemma
Hamel bases
The continuum hypothesis
Ultrafilters on w Families of sets The Banach-Tarski paradox Stationary sets in w1
Stationary sets in larger cardinals
Canonical functions
Infinite graphs
Partition relations
\triangle-systems
Set mappings
Trees
The measure problem
Stationary sets
The axiom of choice Well founded sets and the axiom of foundation
Appendix
Glossary of Concepts
Glossary of Symbols
Index.

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