Zermelo's Axiom of Choice

Zermelo's Axiom of Choice : Its Origins, Development, and Influence

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The Axiom of Choice is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma). This treatment is the only full-length history of the axiom in English, and is much more complete than the two other books on the subject, one in French and the other in Russian. This book covers the Axiom's prehistory of implicit uses in the 19th century, its explicit formulation by Zermelo in 1904, the firestorm of controversy that it caused -- in England, France, Germany, Italy, and the U.S. -- its role in stimulating his axiomatization of set theory in 1908, and its proliferating uses all over mathematics throughout the 20th century.
The book is written so as to be accessible to the advanced mathematics undergraduate, but equally to be informative and stimulating to the professional mathematician. Most technical terms are defined in footnotes, making it accessible by students of the philosophy of mathematics as well.
This new edition has an expanded bibliography and a new preface examining developments since its original 1982 publication.
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Product details

  • Paperback | 448 pages
  • 156 x 235 x 22.86mm | 589.67g
  • New York, United States
  • English
  • 0486488411
  • 9780486488417
  • 632,925

Table of contents

List of SymbolsPrologue1. The Prehistory of the Axiom of Choice2. Zermelo and His Critics (1904-1908)3. Zermelo's Axiom and Axiomatization in Transition (1908-1918)4. The Warsaw School, Widening Applications, Models of Set Theory (1918-1940)Epilogue: After GödelConclusionAppendix 1. Five Letters on Set TheoryAppendix 2. Deductive Relations Concerning the Axiom of ChoiceJournal Abbreviations Used in the BibliographyBibliographyIndex of Numbered PropositionsGeneral Index
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