Axiom of Choice

Axiom of Choice

Author: Horst Herrlich

Publisher: Springer Science & Business Media

ISBN: 9783540309895

Category: Mathematics

Page: 194

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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.
Consequences of the Axiom of Choice
Language: en
Pages: 432
Authors: Paul Howard, Jean E. Rubin
Categories: Mathematics
Type: BOOK - Published: 1998 - Publisher: American Mathematical Soc.

This book, ""Consequences of the Axiom of Choice"", is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing
Axiom of Choice
Language: en
Pages: 194
Authors: Horst Herrlich
Categories: Mathematics
Type: BOOK - Published: 2006-05-11 - Publisher: Springer Science & Business Media

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
The Axiom of Choice
Language: en
Pages: 224
Authors: Thomas J. Jech
Categories: Mathematics
Type: BOOK - Published: 2013-04-09 - Publisher: Courier Corporation

Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Equivalents of the Axiom of Choice, II
Language: en
Pages: 321
Authors: H. Rubin, J.E. Rubin
Categories: Mathematics
Type: BOOK - Published: 1985-03-01 - Publisher: Elsevier

This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and
Equivalents of the Axiom of Choice
Language: en
Pages: 134
Authors: Herman Rubin, Jean E. Rubin
Categories: Axiom of choice
Type: BOOK - Published: 1963 - Publisher: Elsevier

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