Axiom of Choice: 1876 - Brossura

Herrlich, Horst

 
9783540309895: Axiom of Choice: 1876
Brossura
ISBN 10: 3540309896 ISBN 13: 9783540309895
Casa editrice: Springer, 2009

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Dalla quarta di copertina

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.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer
Data di pubblicazione
2009
Lingua
Inglese
ISBN 10 
3540309896
ISBN 13 
9783540309895
Rilegatura
Copertina flessibile
Numero di pagine
206
Contatto del produttore
non disponibile
Persona responsabile
ProductSafety@springernature.com
ProductSafety@springernature.com

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