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Axiom of Choice
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Axiom of Choice Paperback - 2006

by Horst Herrlich


From the publisher

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.

From the rear cover

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:

  1. Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).
  2. Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).
  3. 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.

Details

  • Title Axiom of Choice
  • Author Horst Herrlich
  • Binding Paperback
  • Edition First Edition
  • Pages 198
  • Volumes 1
  • Language ENG
  • Publisher Springer, New York
  • Date 2006-05-11
  • Illustrated Yes
  • ISBN 9783540309895 / 3540309896
  • Weight 0.68 lbs (0.31 kg)
  • Dimensions 9.21 x 6.14 x 0.46 in (23.39 x 15.60 x 1.17 cm)
  • Dewey Decimal Code 511.3
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Axiom of Choice
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Axiom of Choice

by Horst Herrlich

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Axiom of Choice
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Axiom of Choice

by Horst Herrlich

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Paperback / softback. New. AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. 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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Axiom of Choice (Lecture Notes in Mathematics, Vol. 1876) (Lecture Notes in Mathematics, 1876)
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Axiom of Choice (Lecture Notes in Mathematics, Vol. 1876) (Lecture Notes in Mathematics, 1876)

by Herrlich, Horst

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Axiom of Choice (Lecture Notes in Mathematics, Vol. 1876)
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Axiom of Choice (Lecture Notes in Mathematics, Vol. 1876)

by Herrlich, Horst

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