Continuum hypothesis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Continuum hypothesis" in English language version.

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ams.org

mathscinet.ams.org

Goodman, Nicolas D. (1979). "Mathematics as an objective science". The American Mathematical Monthly. 86 (7): 540–551. doi:10.2307/2320581. JSTOR 2320581. MR 0542765. This view is often called formalism. Positions more or less like this may be found in Haskell Curry [5], Abraham Robinson [17], and Paul Cohen [4].
Bagemihl, F. (1989–1990). "Throwing a dart at Freiling's argument against the continuum hypothesis". Real Analysis Exchange. 15 (1): 342–345. doi:10.2307/44152014. JSTOR 44152014. MR 1042552.
Moore, Gregory H. (2011). "Early history of the generalized continuum hypothesis: 1878–1938". Bulletin of Symbolic Logic. 17 (4): 489–532. doi:10.2178/bsl/1318855631. MR 2896574.
Merimovich, Carmi (2007). "A power function with a fixed finite gap everywhere". Journal of Symbolic Logic. 72 (2): 361–417. arXiv:math/0005179. doi:10.2178/jsl/1185803615. MR 2320282. S2CID 15577499.

ams.org

Woodin, W. Hugh (2001). "The Continuum Hypothesis, Part I" (PDF). Notices of the AMS. 48 (6): 567–576. Archived (PDF) from the original on 2022-10-10.
Woodin, W. Hugh (2001). "The Continuum Hypothesis, Part II" (PDF). Notices of the AMS. 48 (7): 681–690. Archived (PDF) from the original on 2022-10-10.

archive.org

Dauben, Joseph Warren (1990). Georg Cantor: His mathematics and philosophy of the infinite. Princeton University Press. pp. 134–137. ISBN 9780691024479.

arxiv.org

Hamkins, Joel David (January 2015). "Is the Dream Solution of the Continuum Hypothesis Attainable?". Notre Dame Journal of Formal Logic. 56 (1). arXiv:1203.4026. doi:10.1215/00294527-2835047.
Hamkins, Joel David (2012). "The set-theoretic multiverse". The Review of Symbolic Logic. 5 (3): 416–449. arXiv:1108.4223. doi:10.1017/S1755020311000359. S2CID 33807508.
Shelah, Saharon (2003). "Logical dreams". Bulletin of the American Mathematical Society. New Series. 40 (2): 203–228. arXiv:math/0211398. doi:10.1090/s0273-0979-03-00981-9. S2CID 1510438.
Merimovich, Carmi (2007). "A power function with a fixed finite gap everywhere". Journal of Symbolic Logic. 72 (2): 361–417. arXiv:math/0005179. doi:10.2178/jsl/1185803615. MR 2320282. S2CID 15577499.

biodiversitylibrary.org

Jourdain, Philip E.B. (1905). "On transfinite cardinal numbers of the exponential form". Philosophical Magazine. Series 6. 9 (49): 42–56. doi:10.1080/14786440509463254.

digizeitschriften.de

Cantor, Georg (1878). "Ein Beitrag zur Mannigfaltigkeitslehre". Journal für die Reine und Angewandte Mathematik. 1878 (84): 242–258. doi:10.1515/crll.1878.84.242 (inactive 1 November 2024).{{cite journal}}: CS1 maint: DOI inactive as of November 2024 (link)

doi.org

Cantor, Georg (1878). "Ein Beitrag zur Mannigfaltigkeitslehre". Journal für die Reine und Angewandte Mathematik. 1878 (84): 242–258. doi:10.1515/crll.1878.84.242 (inactive 1 November 2024).{{cite journal}}: CS1 maint: DOI inactive as of November 2024 (link)
Cohen, Paul J. (15 December 1963). "The independence of the Continuum Hypothesis, [part I]". Proceedings of the National Academy of Sciences of the United States of America. 50 (6): 1143–1148. Bibcode:1963PNAS...50.1143C. doi:10.1073/pnas.50.6.1143. JSTOR 71858. PMC 221287. PMID 16578557.
Gödel, Kurt (1938). "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". Proceedings of the National Academy of Sciences. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.
Cohen, Paul J. (15 January 1964). "The independence of the Continuum Hypothesis, [part] II". Proceedings of the National Academy of Sciences of the United States of America. 51 (1): 105–110. Bibcode:1964PNAS...51..105C. doi:10.1073/pnas.51.1.105. JSTOR 72252. PMC 300611. PMID 16591132.
Feferman, Solomon (February 1999). "Does mathematics need new axioms?". American Mathematical Monthly. 106 (2): 99–111. CiteSeerX 10.1.1.37.295. doi:10.2307/2589047. JSTOR 2589047.
Goodman, Nicolas D. (1979). "Mathematics as an objective science". The American Mathematical Monthly. 86 (7): 540–551. doi:10.2307/2320581. JSTOR 2320581. MR 0542765. This view is often called formalism. Positions more or less like this may be found in Haskell Curry [5], Abraham Robinson [17], and Paul Cohen [4].
Maddy 1988, p. 500. Maddy, Penelope (June 1988). "Believing the axioms, [part I]". Journal of Symbolic Logic. 53 (2). Association for Symbolic Logic: 481–511. doi:10.2307/2274520. JSTOR 2274520.
Freiling, Chris (1986). "Axioms of Symmetry: Throwing darts at the real number line". Journal of Symbolic Logic. 51 (1). Association for Symbolic Logic: 190–200. doi:10.2307/2273955. JSTOR 2273955. S2CID 38174418.
Bagemihl, F. (1989–1990). "Throwing a dart at Freiling's argument against the continuum hypothesis". Real Analysis Exchange. 15 (1): 342–345. doi:10.2307/44152014. JSTOR 44152014. MR 1042552.
Hamkins, Joel David (January 2015). "Is the Dream Solution of the Continuum Hypothesis Attainable?". Notre Dame Journal of Formal Logic. 56 (1). arXiv:1203.4026. doi:10.1215/00294527-2835047.
Rittberg, Colin J. (March 2015). "How Woodin changed his mind: new thoughts on the Continuum Hypothesis". Archive for History of Exact Sciences. 69 (2): 125–151. doi:10.1007/s00407-014-0142-8. S2CID 122205863.
Hamkins, Joel David (2012). "The set-theoretic multiverse". The Review of Symbolic Logic. 5 (3): 416–449. arXiv:1108.4223. doi:10.1017/S1755020311000359. S2CID 33807508.
Shelah, Saharon (2003). "Logical dreams". Bulletin of the American Mathematical Society. New Series. 40 (2): 203–228. arXiv:math/0211398. doi:10.1090/s0273-0979-03-00981-9. S2CID 1510438.
Jourdain, Philip E.B. (1905). "On transfinite cardinal numbers of the exponential form". Philosophical Magazine. Series 6. 9 (49): 42–56. doi:10.1080/14786440509463254.
Moore, Gregory H. (2011). "Early history of the generalized continuum hypothesis: 1878–1938". Bulletin of Symbolic Logic. 17 (4): 489–532. doi:10.2178/bsl/1318855631. MR 2896574.
Gillman, Leonard (2002). "Two classical surprises concerning the Axiom of Choice and the Continuum Hypothesis" (PDF). American Mathematical Monthly. 109 (6): 544–553. doi:10.2307/2695444. JSTOR 2695444. Archived (PDF) from the original on 2022-10-10.
Merimovich, Carmi (2007). "A power function with a fixed finite gap everywhere". Journal of Symbolic Logic. 72 (2): 361–417. arXiv:math/0005179. doi:10.2178/jsl/1185803615. MR 2320282. S2CID 15577499.

ghostarchive.org

Woodin, W. Hugh (2001). "The Continuum Hypothesis, Part I" (PDF). Notices of the AMS. 48 (6): 567–576. Archived (PDF) from the original on 2022-10-10.
Woodin, W. Hugh (2001). "The Continuum Hypothesis, Part II" (PDF). Notices of the AMS. 48 (7): 681–690. Archived (PDF) from the original on 2022-10-10.
Foreman, Matt (2003). "Has the Continuum Hypothesis been settled?" (PDF). Archived (PDF) from the original on 2022-10-10. Retrieved 25 February 2006.
Feferman, Solomon (2011). "Is the Continuum Hypothesis a definite mathematical problem?" (PDF). Exploring the Frontiers of Independence. Harvard lecture series. Archived (PDF) from the original on 2022-10-10.
Gillman, Leonard (2002). "Two classical surprises concerning the Axiom of Choice and the Continuum Hypothesis" (PDF). American Mathematical Monthly. 109 (6): 544–553. doi:10.2307/2695444. JSTOR 2695444. Archived (PDF) from the original on 2022-10-10.

harvard.edu

ui.adsabs.harvard.edu

Cohen, Paul J. (15 December 1963). "The independence of the Continuum Hypothesis, [part I]". Proceedings of the National Academy of Sciences of the United States of America. 50 (6): 1143–1148. Bibcode:1963PNAS...50.1143C. doi:10.1073/pnas.50.6.1143. JSTOR 71858. PMC 221287. PMID 16578557.
Gödel, Kurt (1938). "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". Proceedings of the National Academy of Sciences. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.
Cohen, Paul J. (15 January 1964). "The independence of the Continuum Hypothesis, [part] II". Proceedings of the National Academy of Sciences of the United States of America. 51 (1): 105–110. Bibcode:1964PNAS...51..105C. doi:10.1073/pnas.51.1.105. JSTOR 72252. PMC 300611. PMID 16591132.

logic.harvard.edu

Koellner, Peter (2011). "The Continuum Hypothesis" (PDF). Exploring the Frontiers of Independence. Harvard lecture series. Archived (PDF) from the original on 2012-01-24.
Koellner, Peter (2011). "Feferman on the indefiniteness of CH" (PDF). Archived (PDF) from the original on 2012-03-19.

helsinki.fi

math.helsinki.fi

Foreman, Matt (2003). "Has the Continuum Hypothesis been settled?" (PDF). Archived (PDF) from the original on 2022-10-10. Retrieved 25 February 2006.

jstor.org

Cohen, Paul J. (15 December 1963). "The independence of the Continuum Hypothesis, [part I]". Proceedings of the National Academy of Sciences of the United States of America. 50 (6): 1143–1148. Bibcode:1963PNAS...50.1143C. doi:10.1073/pnas.50.6.1143. JSTOR 71858. PMC 221287. PMID 16578557.
Cohen, Paul J. (15 January 1964). "The independence of the Continuum Hypothesis, [part] II". Proceedings of the National Academy of Sciences of the United States of America. 51 (1): 105–110. Bibcode:1964PNAS...51..105C. doi:10.1073/pnas.51.1.105. JSTOR 72252. PMC 300611. PMID 16591132.
Feferman, Solomon (February 1999). "Does mathematics need new axioms?". American Mathematical Monthly. 106 (2): 99–111. CiteSeerX 10.1.1.37.295. doi:10.2307/2589047. JSTOR 2589047.
Goodman, Nicolas D. (1979). "Mathematics as an objective science". The American Mathematical Monthly. 86 (7): 540–551. doi:10.2307/2320581. JSTOR 2320581. MR 0542765. This view is often called formalism. Positions more or less like this may be found in Haskell Curry [5], Abraham Robinson [17], and Paul Cohen [4].
Maddy 1988, p. 500. Maddy, Penelope (June 1988). "Believing the axioms, [part I]". Journal of Symbolic Logic. 53 (2). Association for Symbolic Logic: 481–511. doi:10.2307/2274520. JSTOR 2274520.
Freiling, Chris (1986). "Axioms of Symmetry: Throwing darts at the real number line". Journal of Symbolic Logic. 51 (1). Association for Symbolic Logic: 190–200. doi:10.2307/2273955. JSTOR 2273955. S2CID 38174418.
Bagemihl, F. (1989–1990). "Throwing a dart at Freiling's argument against the continuum hypothesis". Real Analysis Exchange. 15 (1): 342–345. doi:10.2307/44152014. JSTOR 44152014. MR 1042552.
Gillman, Leonard (2002). "Two classical surprises concerning the Axiom of Choice and the Continuum Hypothesis" (PDF). American Mathematical Monthly. 109 (6): 544–553. doi:10.2307/2695444. JSTOR 2695444. Archived (PDF) from the original on 2022-10-10.

maa.org

Gillman, Leonard (2002). "Two classical surprises concerning the Axiom of Choice and the Continuum Hypothesis" (PDF). American Mathematical Monthly. 109 (6): 544–553. doi:10.2307/2695444. JSTOR 2695444. Archived (PDF) from the original on 2022-10-10.

nih.gov

ncbi.nlm.nih.gov

Cohen, Paul J. (15 December 1963). "The independence of the Continuum Hypothesis, [part I]". Proceedings of the National Academy of Sciences of the United States of America. 50 (6): 1143–1148. Bibcode:1963PNAS...50.1143C. doi:10.1073/pnas.50.6.1143. JSTOR 71858. PMC 221287. PMID 16578557.
Gödel, Kurt (1938). "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". Proceedings of the National Academy of Sciences. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.
Cohen, Paul J. (15 January 1964). "The independence of the Continuum Hypothesis, [part] II". Proceedings of the National Academy of Sciences of the United States of America. 51 (1): 105–110. Bibcode:1964PNAS...51..105C. doi:10.1073/pnas.51.1.105. JSTOR 72252. PMC 300611. PMID 16591132.

pubmed.ncbi.nlm.nih.gov

Cohen, Paul J. (15 December 1963). "The independence of the Continuum Hypothesis, [part I]". Proceedings of the National Academy of Sciences of the United States of America. 50 (6): 1143–1148. Bibcode:1963PNAS...50.1143C. doi:10.1073/pnas.50.6.1143. JSTOR 71858. PMC 221287. PMID 16578557.
Gödel, Kurt (1938). "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". Proceedings of the National Academy of Sciences. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.
Cohen, Paul J. (15 January 1964). "The independence of the Continuum Hypothesis, [part] II". Proceedings of the National Academy of Sciences of the United States of America. 51 (1): 105–110. Bibcode:1964PNAS...51..105C. doi:10.1073/pnas.51.1.105. JSTOR 72252. PMC 300611. PMID 16591132.

projecteuclid.org

Bagemihl, F. (1989–1990). "Throwing a dart at Freiling's argument against the continuum hypothesis". Real Analysis Exchange. 15 (1): 342–345. doi:10.2307/44152014. JSTOR 44152014. MR 1042552.

psu.edu

citeseerx.ist.psu.edu

Feferman, Solomon (February 1999). "Does mathematics need new axioms?". American Mathematical Monthly. 106 (2): 99–111. CiteSeerX 10.1.1.37.295. doi:10.2307/2589047. JSTOR 2589047.

quantamagazine.org

Wolchover, Natalie (15 July 2021). "How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer". Quanta Magazine. Retrieved 30 December 2021.

semanticscholar.org

api.semanticscholar.org

Freiling, Chris (1986). "Axioms of Symmetry: Throwing darts at the real number line". Journal of Symbolic Logic. 51 (1). Association for Symbolic Logic: 190–200. doi:10.2307/2273955. JSTOR 2273955. S2CID 38174418.
Rittberg, Colin J. (March 2015). "How Woodin changed his mind: new thoughts on the Continuum Hypothesis". Archive for History of Exact Sciences. 69 (2): 125–151. doi:10.1007/s00407-014-0142-8. S2CID 122205863.
Hamkins, Joel David (2012). "The set-theoretic multiverse". The Review of Symbolic Logic. 5 (3): 416–449. arXiv:1108.4223. doi:10.1017/S1755020311000359. S2CID 33807508.
Shelah, Saharon (2003). "Logical dreams". Bulletin of the American Mathematical Society. New Series. 40 (2): 203–228. arXiv:math/0211398. doi:10.1090/s0273-0979-03-00981-9. S2CID 1510438.
Merimovich, Carmi (2007). "A power function with a fixed finite gap everywhere". Journal of Symbolic Logic. 72 (2): 361–417. arXiv:math/0005179. doi:10.2178/jsl/1185803615. MR 2320282. S2CID 15577499.

stackexchange.com

math.stackexchange.com

Asaf Karagila (https://math.stackexchange.com/users/622/asaf-karagila), How to formulate continuum hypothesis without the axiom of choice?, URL (version: 2017-04-13): https://math.stackexchange.com/q/404813

stanford.edu

math.stanford.edu

Feferman, Solomon (2011). "Is the Continuum Hypothesis a definite mathematical problem?" (PDF). Exploring the Frontiers of Independence. Harvard lecture series. Archived (PDF) from the original on 2022-10-10.

web.archive.org

Koellner, Peter (2011). "The Continuum Hypothesis" (PDF). Exploring the Frontiers of Independence. Harvard lecture series. Archived (PDF) from the original on 2012-01-24.
Koellner, Peter (2011). "Feferman on the indefiniteness of CH" (PDF). Archived (PDF) from the original on 2012-03-19.