Thomas Jech’s The Axiom of Choice is, in its Dover edition, a reprint of the classic which explains the place of the Axiom of Choice in. Thomas Jech is a set theorist and logician, who among many other things wrote a classic book on the Axiom of Choice (AC). I strongly recommend this book for. The Axiom of Choice: A nonmeasurable set of real numbers: A paradoxical decomposition of the sphere: Problems: Historical.
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The Axiom of Choice
The Axiom of Choice. Description Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths thw consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.
The Axiom of Choice
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 show more.
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Table of contents Preface1. Use of the axiom of choice3. Consistency of the axiom of choice4. Independence adiom the axiom of choice6. Models with finite supports8. Some weaker versions of the axiom of choice9. Cardinal numbers in set theory without choice Some properties contradicting the axiom of choiceAppendix 1. Equivalents of the axiom of choiceAppendix 2.
Equivalents of the Prime Ideal TheoremAppendix 3. Various independence resultsAppendix 4.
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