Axiom of Choice

Axiom of Choice

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Cod produs/ISBN: 9783540309895

Disponibilitate: Acest produs nu este momentan in stoc

Editura: Springer

Limba: Engleza

Nr. pagini: 198

Coperta: Paperback

Dimensiuni: 15.5 x 1.2 x 23.5 cm

An aparitie: 2006

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.  

  3. Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).
  4.  

  5. 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.


Springer
An aparitie 2006
Autor Horst Herrlich
Dimensiuni 15.5 x 1.2 x 23.5 cm
Editura Springer
Format Paperback
ISBN 9783540309895
Limba Engleza
Nr pag 198

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