Problems and Theorems in Classical Set Theory

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This is the first comprehensive collection of problems in set theory. It contains well chosen sequences of exercises. Most of the problems are challenging and require work, wit, and inspiration. The book is destined to become a classic.
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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.- riangle 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.- riangle-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.
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.

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Autor: Peter Komjath
ISBN-13 :: 9781441921406
ISBN: 1441921400
Erscheinungsjahr: 24.11.2010
Verlag: Springer New York
Gewicht: 779g
Seiten: 528
Sprache: Englisch
Auflage Softcover reprint of hardcover 1st ed. 2006.
Sonstiges: Taschenbuch, 238x157x33 mm
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