Problems and Theorems in Classical Set Theory

Problems and Theorems in Classical Set Theory
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Artikel-Nr:
9781441921406
Veröffentl:
2010
Einband:
Paperback
Erscheinungsdatum:
24.11.2010
Seiten:
528
Autor:
Vilmos Totik
Gewicht:
791 g
Format:
235x155x28 mm
Serie:
Problem Books in Mathematics
Sprache:
Englisch
Beschreibung:

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.

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.
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 ?.- Families of sets.- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^

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