The Axiom of Choice

Nonfiction, Science & Nature, Mathematics, Logic
Cover of the book The Axiom of Choice by Thomas J. Jech, Dover Publications
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Author: Thomas J. Jech ISBN: 9780486318257
Publisher: Dover Publications Publication: April 9, 2013
Imprint: Dover Publications Language: English
Author: Thomas J. Jech
ISBN: 9780486318257
Publisher: Dover Publications
Publication: April 9, 2013
Imprint: Dover Publications
Language: English
Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.
An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics
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Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.
An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics

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