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Zermelo's axiom of choice : its origins, development, and influence

Verfasser/in: Gregory H Moore
Verlag: New York : Springer-Verlag, ©1982.
Serien: Studies in the history of mathematics and physical sciences, 8.
Ausgabe/Format   Print book : EnglischAlle Ausgaben und Formate anzeigen
Datenbank:WorldCat
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Physisches Format Online version:
Moore, Gregory H.
Zermelo's axiom of choice.
New York : Springer-Verlag, ©1982
(OCoLC)625026783
Name: Ernst Zermelo; Ernst Zermelo; Ernst Zermelo; Ernst Zermelo; Ernst Zermelo
Medientyp: Internetquelle
Dokumenttyp: Buch, Internet-Ressource
Alle Autoren: Gregory H Moore
ISBN: 0387906703 9780387906706 3540906703 9783540906704
OCLC-Nummer: 8626900
Anmerkungen: Includes indexes.
Beschreibung: xiv, 410 pages : illustrations ; 25 cm.
Inhalt: Prologue.- 1 The Prehistory of the Axiom of Choice.- 1.1 Introduction.- 1.2 The Origins of the Assumption.- 1.3 The Boundary between the Finite and the Infinite.- 1.4 Cantor's Legacy of Implicit Uses.- 1.5 The Well-Ordering Problem and the Continuum Hypothesis.- 1.6 The Reception of the Well-Ordering Problem.- 1.7 Implicit Uses by Future Critics.- 1.8 Italian Objections to Arbitrary Choices.- 1.9 Retrospect and Prospect.- 2 Zermelo and His Critics (1904-1908).- 2.1 Konig's "Refutation" of the Continuum Hypothesis.- 2.2 Zermelo's Proof of the Well-Ordering Theorem.- 2.3 French Constructivist Reaction.- 2.4 A Matter of Definitions: Richard, Poincare, and Frechet.- 2.5 The German Cantorians.- 2.6 Father and Son: Julius and Denes Konig.- 2.7 An English Debate.- 2.8 Peano: Logic vs. Zermelo's Axiom.- 2.9 Brouwer: A Voice in the Wilderness.- 2.10 Enthusiasm and Mistrust in America.- 2.11 Retrospect and Prospect.- 3 Zermelo's Axiom and Axiomatization in Transition (1908-1918).- 3.1 Zermelo's Reply to His Critics.- 3.2 Zermelo's Axiomatization of Set Theory.- 3.3 The Ambivalent Response to the Axiomatization.- 3.4 The Trichotomy of Cardinals and Other Equivalents.- 3.5 Steinitz and Algebraic Applications.- 3.6 A Smoldering Controversy.- 3.7 Hausdorff's Paradox.- 3.8 An Abortive Attempt to Prove the Axiom of Choice.- 3.9 Retrospect and Prospect.- 4 The Warsaw School, Widening Applications, Models of Set Theory (1918-1940).- 4.1 A Survey by Sierpi?ski.- 4.2 Finite, Infinite, and Mediate.- 4.3 Cardinal Equivalents.- 4.4 Zorn's Lemma and Related Principles.- 4.5 Widening Applications in Algebra.- 4.6 Convergence and Compactness in General Topology.- 4.7 Negations and Alternatives.- 4.8 The Axiom's Contribution to Logic.- 4.9 Shifting Axiomatizations for Set Theory.- 4.10 Consistency and Independence of the Axiom.- 4.11 Scepticism and Inquiry.- 4.12 Retrospect and Prospect.- Epilogue: After Godel.- 5.1 A Period of Stability: 1940-1963.- 5.2 Cohen's Legacy.- Conclusion.- 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.- General Index.
Serientitel: Studies in the history of mathematics and physical sciences, 8.
Verfasserangabe: Gregory H. Moore.

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