skip to content
Zermelo's axiom of choice. Preview this item
ClosePreview this item
Checking...

Zermelo's axiom of choice.

Author: Gregory H Moore
Publisher: New York, Heidelberg, Berlin : Springer, 1982.
Series: Studies in the history of mathematics and physical sciences, 8.
Edition/Format:   Print book : EnglishView all editions and formats
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: Gregory H Moore
ISBN: 0387906703 9780387906706 3540906703 9783540906704
OCLC Number: 252031610
Description: XIV, 410 Seiten ; 8°.
Contents: 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.
Series Title: Studies in the history of mathematics and physical sciences, 8.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/252031610> # Zermelo's axiom of choice.
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "252031610" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/795278830#Place/new_york_heidelberg_berlin> ; # New York, Heidelberg, Berlin
   schema:about <http://experiment.worldcat.org/entity/work/data/795278830#Topic/auswahlaxiom> ; # Auswahlaxiom
   schema:about <http://experiment.worldcat.org/entity/work/data/795278830#Topic/philosophie_menge> ; # Philosophie--Menge
   schema:about <http://experiment.worldcat.org/entity/work/data/795278830#Topic/menge_philosophie> ; # Menge--Philosophie
   schema:about <http://experiment.worldcat.org/entity/work/data/795278830#Topic/geschichte> ; # Geschichte
   schema:bookFormat bgn:PrintBook ;
   schema:creator <http://viaf.org/viaf/264686341> ; # Gregory H. Moore
   schema:datePublished "1982" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/795278830> ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/795278830#Series/studies_in_the_history_of_mathematics_and_physical_sciences> ; # Studies in the history of mathematics and physical sciences ;
   schema:name "Zermelo's axiom of choice." ;
   schema:productID "252031610" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/252031610#PublicationEvent/new_york_heidelberg_berlin_springer_1982> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/795278830#Agent/springer> ; # Springer
   schema:workExample <http://worldcat.org/isbn/9783540906704> ;
   schema:workExample <http://worldcat.org/isbn/9780387906706> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/252031610> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/795278830#Place/new_york_heidelberg_berlin> # New York, Heidelberg, Berlin
    a schema:Place ;
   schema:name "New York, Heidelberg, Berlin" ;
    .

<http://experiment.worldcat.org/entity/work/data/795278830#Series/studies_in_the_history_of_mathematics_and_physical_sciences> # Studies in the history of mathematics and physical sciences ;
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/252031610> ; # Zermelo's axiom of choice.
   schema:name "Studies in the history of mathematics and physical sciences ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/795278830#Topic/menge_philosophie> # Menge--Philosophie
    a schema:Intangible ;
   schema:name "Menge--Philosophie" ;
    .

<http://experiment.worldcat.org/entity/work/data/795278830#Topic/philosophie_menge> # Philosophie--Menge
    a schema:Intangible ;
   schema:name "Philosophie--Menge" ;
    .

<http://viaf.org/viaf/264686341> # Gregory H. Moore
    a schema:Person ;
   schema:familyName "Moore" ;
   schema:givenName "Gregory H." ;
   schema:name "Gregory H. Moore" ;
    .

<http://worldcat.org/isbn/9780387906706>
    a schema:ProductModel ;
   schema:isbn "0387906703" ;
   schema:isbn "9780387906706" ;
    .

<http://worldcat.org/isbn/9783540906704>
    a schema:ProductModel ;
   schema:isbn "3540906703" ;
   schema:isbn "9783540906704" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.