Erschienen: 11.05.2006 Abbildung von Herrlich | Axiom of Choice | 2006 | 1876

Herrlich

Axiom of Choice

lieferbar ca. 10 Tage als Sonderdruck ohne Rückgaberecht

2006. Buch. XIV, 198 S. 1 s/w-Abbildung, 1 s/w-Tabelle, Bibliographien. Softcover

Springer. ISBN 978-3-540-30989-5

Format (B x L): 15,5 x 23,3 cm

Gewicht: 690 g

In englischer Sprache

Das Werk ist Teil der Reihe: Lecture Notes in Mathematics; 1876

Produktbeschreibung

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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