Equivalents of the Axiom of Choice, II

Equivalents of the Axiom of Choice, II

Author: H. Rubin

Publisher: Elsevier

ISBN: 0080887651

Category: Mathematics

Page: 321

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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 a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles.
The Axiom of Choice
Language: en
Pages: 226
Authors: Thomas J. Jech
Categories: Mathematics
Type: BOOK - Published: 2008-01-01 - 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.
Axiom of Choice
Language: en
Pages: 207
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. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from
Annals of Mathematics Studies
Language: en
Pages: 86
Authors: Kurt Gödel
Categories: Logic, Symbolic and mathematical
Type: BOOK - Published: 1940 - Publisher:

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Zermelo's Axiom of Choice
Language: en
Pages: 450
Authors: Gregory H. Moore
Categories: Mathematics
Type: BOOK - Published: 2012-09-20 - Publisher: Courier Corporation

"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--
Elements of Abstract Analysis
Language: en
Pages: 318
Authors: Mícheál O'Searcoid
Categories: Mathematics
Type: BOOK - Published: 2001-11-09 - Publisher: Springer Science & Business Media

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students