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Axiom of Choice
Paperback
Series: Lecture Notes in Mathematics, Book 1876
FictionAlgebraGeneral Mathematics
ISBN13: 9783540309895
Publisher: Springer
Published: May 11 2006
Pages: 198
Weight: 0.68
Height: 0.46 Width: 6.14 Depth: 9.21
Language: English
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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