Auswahlaxiom (German Wikipedia)

Analysis of information sources in references of the Wikipedia article "Auswahlaxiom" in German language version.

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arxiv.org

We have seen that in every major theory of physics, challenging mathematical questions arise from the assumption that spacetime is a continuum. Zitiert in John Baez: Struggles with the Continuum. 2020, doi:10.48550/arXiv.1609.01421, arxiv:1609.01421 [math-ph], Kap. 6: Conclusions, S. 35.

doi.org

Andreas Blass: Existence of bases implies the axiom of choice. In: Contemporary Mathematics. Band 31: Axiomatic set theory. 1984, ISBN 0-8218-5026-1, S. 31–33, doi:10.1090/conm/031/763890 (umich.edu [PDF; 182 kB]).
Kurt Gödel: The consistency of the axiom of choice and of the generalized continuum-hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 24, 1938, ISSN 0027-8424, S. 556–557, doi:10.1073/pnas.24.12.556 (pnas.org [PDF; 257 kB]).
Paul Joseph Cohen: The independence of the continuum hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 50, Nr. 6, Dezember 1963, S. 1143–1148, doi:10.1073/pnas.50.6.1143, PMID 16578557, PMC 221287 (freier Volltext), bibcode:1963PNAS...50.1143C (englisch).
Paul Joseph Cohen: The independence of the continuum hypothesis, II. In: Proceedings of the National Academy of Sciences of the United States of America. Band 51, Nr. 1, Januar 1964, S. 105–110, doi:10.1073/pnas.51.1.105, PMID 16591132, PMC 300611 (freier Volltext), bibcode:1964PNAS...51..105C (englisch).
Paul Cohen: Set Theory and the Continuum Hypothesis. W. A. Benjamin, New York 1966, OCLC 291078 (englisch, Scan der Neuauflage, Courier Corporation, 2008 in der Google-Buchsuche).
Eine längere Übersicht an „Pro und Kontra“ findet man u. a. in Horst Herrlich: Axiom of Choice. Springer Lecture Notes in Mathematics, 1876. Springer Verlag, Berlin/Heidelberg 2006, ISBN 3-540-30989-6, Kap.: Disasters without Choice, S. 43–141, doi:10.1007/11601562.
Robert M. Solovay: A model of set-theory in which every set of reals is Lebesgue measurable. In: Annals of Mathematics. Series 2, Band 92. 1970, S. 1–56, doi:10.2307/1970696, JSTOR:1970696.
We have seen that in every major theory of physics, challenging mathematical questions arise from the assumption that spacetime is a continuum. Zitiert in John Baez: Struggles with the Continuum. 2020, doi:10.48550/arXiv.1609.01421, arxiv:1609.01421 [math-ph], Kap. 6: Conclusions, S. 35.
Janus-faced nature, zitiert in Horst Herrlich: Axiom of Choice. Springer Lecture Notes in Mathematics, 1876. Springer Verlag, Berlin/Heidelberg 2006, ISBN 3-540-30989-6, S. 137, doi:10.1007/11601562.

google.de

books.google.de

Paul Joseph Cohen: The independence of the continuum hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 50, Nr. 6, Dezember 1963, S. 1143–1148, doi:10.1073/pnas.50.6.1143, PMID 16578557, PMC 221287 (freier Volltext), bibcode:1963PNAS...50.1143C (englisch).
Paul Joseph Cohen: The independence of the continuum hypothesis, II. In: Proceedings of the National Academy of Sciences of the United States of America. Band 51, Nr. 1, Januar 1964, S. 105–110, doi:10.1073/pnas.51.1.105, PMID 16591132, PMC 300611 (freier Volltext), bibcode:1964PNAS...51..105C (englisch).
Paul Cohen: Set Theory and the Continuum Hypothesis. W. A. Benjamin, New York 1966, OCLC 291078 (englisch, Scan der Neuauflage, Courier Corporation, 2008 in der Google-Buchsuche).

harvard.edu

ui.adsabs.harvard.edu

Paul Joseph Cohen: The independence of the continuum hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 50, Nr. 6, Dezember 1963, S. 1143–1148, doi:10.1073/pnas.50.6.1143, PMID 16578557, PMC 221287 (freier Volltext), bibcode:1963PNAS...50.1143C (englisch).
Paul Joseph Cohen: The independence of the continuum hypothesis, II. In: Proceedings of the National Academy of Sciences of the United States of America. Band 51, Nr. 1, Januar 1964, S. 105–110, doi:10.1073/pnas.51.1.105, PMID 16591132, PMC 300611 (freier Volltext), bibcode:1964PNAS...51..105C (englisch).
Paul Cohen: Set Theory and the Continuum Hypothesis. W. A. Benjamin, New York 1966, OCLC 291078 (englisch, Scan der Neuauflage, Courier Corporation, 2008 in der Google-Buchsuche).

jstor.org

Robert M. Solovay: A model of set-theory in which every set of reals is Lebesgue measurable. In: Annals of Mathematics. Series 2, Band 92. 1970, S. 1–56, doi:10.2307/1970696, JSTOR:1970696.

maa.org

Leonard Gillman: Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis. In: American Mathematical Monthly. Band 109, Juni–Juli 2002, S. 544–553, hier S. 544 (maa.org [PDF; 119 kB]).

nih.gov

ncbi.nlm.nih.gov

Paul Joseph Cohen: The independence of the continuum hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 50, Nr. 6, Dezember 1963, S. 1143–1148, doi:10.1073/pnas.50.6.1143, PMID 16578557, PMC 221287 (freier Volltext), bibcode:1963PNAS...50.1143C (englisch).
Paul Joseph Cohen: The independence of the continuum hypothesis, II. In: Proceedings of the National Academy of Sciences of the United States of America. Band 51, Nr. 1, Januar 1964, S. 105–110, doi:10.1073/pnas.51.1.105, PMID 16591132, PMC 300611 (freier Volltext), bibcode:1964PNAS...51..105C (englisch).
Paul Cohen: Set Theory and the Continuum Hypothesis. W. A. Benjamin, New York 1966, OCLC 291078 (englisch, Scan der Neuauflage, Courier Corporation, 2008 in der Google-Buchsuche).

pnas.org

Kurt Gödel: The consistency of the axiom of choice and of the generalized continuum-hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 24, 1938, ISSN 0027-8424, S. 556–557, doi:10.1073/pnas.24.12.556 (pnas.org [PDF; 257 kB]).

umich.edu

dept.math.lsa.umich.edu

Andreas Blass: Existence of bases implies the axiom of choice. In: Contemporary Mathematics. Band 31: Axiomatic set theory. 1984, ISBN 0-8218-5026-1, S. 31–33, doi:10.1090/conm/031/763890 (umich.edu [PDF; 182 kB]).

worldcat.org

Paul Joseph Cohen: The independence of the continuum hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 50, Nr. 6, Dezember 1963, S. 1143–1148, doi:10.1073/pnas.50.6.1143, PMID 16578557, PMC 221287 (freier Volltext), bibcode:1963PNAS...50.1143C (englisch).
Paul Joseph Cohen: The independence of the continuum hypothesis, II. In: Proceedings of the National Academy of Sciences of the United States of America. Band 51, Nr. 1, Januar 1964, S. 105–110, doi:10.1073/pnas.51.1.105, PMID 16591132, PMC 300611 (freier Volltext), bibcode:1964PNAS...51..105C (englisch).
Paul Cohen: Set Theory and the Continuum Hypothesis. W. A. Benjamin, New York 1966, OCLC 291078 (englisch, Scan der Neuauflage, Courier Corporation, 2008 in der Google-Buchsuche).

zdb-katalog.de

Kurt Gödel: The consistency of the axiom of choice and of the generalized continuum-hypothesis. In: Proceedings of the National Academy of Sciences of the United States of America. Band 24, 1938, ISSN 0027-8424, S. 556–557, doi:10.1073/pnas.24.12.556 (pnas.org [PDF; 257 kB]).