Problems and Theorems in Classical Set Theory

 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.