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Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Dover Books on Mathematics)by Gregory H. Moore
Synopses & Reviews
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.
This book chronicles Ernst Zermelo's development of set theory's crucial principle, the axiom of choice, including its initial controversy and its central place in set theory and mathematical logic. 1982 edition.
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.
Table of Contents
List of Symbols
1. The Prehistory of the Axiom of Choice
2. 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 Gödel
Appendix 1. Five Letters on Set Theory
Appendix 2. Deductive Relations Concerning the Axiom of Choice
Journal Abbreviations Used in the Bibliography
Index of Numbered Propositions
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