ENGLISH

Axiom of Choice

By Horst Herrlich (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2006
ISBN
9783540309895, 9783540342687, 3540309896
DOI
10.1007/11601562
ISSN
0075-8434
Open Library ID
OL9056192M
Language
english
Format
PDF
Filesize
1 MB (1322100 bytes)
Series
Lecture Notes in Mathematics 1876
Edition
1
Pages
198\206
Topic
Mathematics Logic
Library
Kolxo3
Time added
2009-07-20 03:45:11
EconomicsMathematical Logic and Foundations; General AlgebrSocial and Behav. Sciences; Combinatorics; Topolog

Description

AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.

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