Editing Continuum hypothesis (section)

==References==
<!-- The use of parenthetical citations is currently deprecated - May 2021 -->
{{reflist|refs=

<ref name=bagemihl>{{cite journal
 | last = Bagemihl | first = F.
 | issue = 1
 | journal = Real Analysis Exchange
 | mr = 1042552
 | pages = 342–345
 | title = Throwing a dart at Freiling's argument against the continuum hypothesis
 | url = https://projecteuclid.org/journals/real-analysis-exchange/volume-15/issue-1/THROWING-A-DART-AT-FREILINGS-ARGUMENT-AGAINST-THE-CONTINUUM-HYPOTHESIS/10.2307/44152014.full
 | volume = 15
 | year = 1989–1990| doi = 10.2307/44152014
 | jstor = 44152014
 }}</ref>

<ref name=Cantor1878>
{{Cite journal
 |last=Cantor |first=Georg  |author-link=Georg Cantor
 |year=1878
 |title=Ein Beitrag zur Mannigfaltigkeitslehre
 |journal=[[Journal für die Reine und Angewandte Mathematik]]
 |volume=1878  |issue=84  |pages=242–258
 |doi=10.1515/crll.1878.84.242
 |doi-broken-date=1 November 2024 |url=http://www.digizeitschriften.de/dms/img/?PPN=PPN243919689_0084&DMDID=dmdlog15
}}
</ref>

<ref name=Gödel1940>
{{Cite book
 |last=Gödel |first=Kurt  |author-link=Kurt Gödel 
 |year=1940
 |title=The Consistency of the Continuum-Hypothesis
 |publisher=Princeton University Press
}}
</ref>

<ref name=Dauben1990_1347>
{{Cite book
 |last=Dauben  |first=Joseph Warren
 |year=1990
 |title=Georg Cantor: His mathematics and philosophy of the infinite
 |pages=[https://archive.org/details/georgcantorhisma0000daub/page/134 134]–137
 |publisher=Princeton University Press
 |isbn=9780691024479
 |url=https://archive.org/details/georgcantorhisma0000daub
 |url-access=registration
}}
</ref>

<ref name=Cohen1963>
{{Cite journal
 |last=Cohen  |first=Paul J.
 |date=15 December 1963
 |title=The independence of the Continuum Hypothesis, [part&nbsp;I]
 |journal=Proceedings of the National Academy of Sciences of the United States of America
 |volume=50  |issue=6  |pages=1143–1148
 |doi=10.1073/pnas.50.6.1143  |pmid=16578557
 |pmc=221287  |jstor=71858  |bibcode=1963PNAS...50.1143C
|doi-access=free
 }}
</ref>

<ref name=Goldrei1996>
{{Cite book
 |last=Goldrei |first=Derek
 |year=1996
 |title=Classic Set Theory
 |publisher=[[Chapman & Hall]]
}}
</ref>

<ref name=Cohen1964>
{{Cite journal
 |last=Cohen |first=Paul J.
 |date=15 January 1964
 |title=The independence of the Continuum Hypothesis, [part]&nbsp;II
 |journal=Proceedings of the National Academy of Sciences of the United States of America
 |volume=51 |issue=1 |pages=105–110
 |doi=10.1073/pnas.51.1.105 |pmid=16591132
 |pmc=300611 |jstor=72252 |bibcode=1964PNAS...51..105C
|doi-access=free
 }}
</ref>

<ref name=Feferman1999_99111>
{{Cite journal
 |last=Feferman |first=Solomon
 |date=February 1999
 |title=Does mathematics need new axioms?
 |journal=American Mathematical Monthly
 |volume=106 |issue=2 |pages=99–111
 |doi=10.2307/2589047 |jstor=2589047
 |citeseerx=10.1.1.37.295
}}
</ref>

<ref name=Woodin2001a>
{{Cite journal
 |last=Woodin |first=W. Hugh
 |year=2001
 |title=The Continuum Hypothesis, Part&nbsp;I
 |journal=Notices of the AMS
 |volume=48 |issue=6 |pages=567–576
 |url=https://www.ams.org/notices/200106/fea-woodin.pdf |archive-url=https://ghostarchive.org/archive/20221010/https://www.ams.org/notices/200106/fea-woodin.pdf |archive-date=2022-10-10 |url-status=live
}}
</ref>

<ref name=Woodin2001b>
{{Cite journal
 |last=Woodin  |first=W. Hugh
 |year=2001
 |title=The Continuum Hypothesis, Part&nbsp;II
 |journal=Notices of the AMS
 |volume=48 |issue=7 |pages=681–690
 |url=https://www.ams.org/notices/200107/fea-woodin.pdf |archive-url=https://ghostarchive.org/archive/20221010/https://www.ams.org/notices/200107/fea-woodin.pdf |archive-date=2022-10-10 |url-status=live
}}
</ref>

<ref name=Koellner2011a>
{{Cite web
 |last=Koellner |first=Peter  |author-link=Peter Koellner
 |year=2011
 |title=The Continuum Hypothesis
 |work=Exploring the Frontiers of Independence
 |series=Harvard lecture series 
 |url=http://logic.harvard.edu/EFI_CH.pdf |archive-url=https://web.archive.org/web/20120124183745/http://logic.harvard.edu/EFI_CH.pdf |archive-date=2012-01-24 |url-status=live
}}
</ref>

<ref name=Koellner2011b>
{{Cite web
 |last=Koellner |first=Peter
 |year=2011
 |title=Feferman on the indefiniteness of CH
 |url=http://logic.harvard.edu/EFI_Feferman_comments.pdf |archive-url=https://web.archive.org/web/20120319061308/http://logic.harvard.edu/EFI_Feferman_comments.pdf |archive-date=2012-03-19 |url-status=live
}}
</ref>

<ref name=Goodman1979>
{{Cite journal
 |last=Goodman  |first=Nicolas D.
 |year=1979
 |title=Mathematics as an objective science
 |journal=The American Mathematical Monthly
 |volume=86  |issue=7  |pages=540–551
 |doi=10.2307/2320581
 |jstor=2320581
 |mr=542765
 |quote=This view is often called ''formalism''. Positions more or less like this may be found in Haskell Curry&nbsp;[5], Abraham Robinson&nbsp;[17], and Paul Cohen&nbsp;[4].
}}
</ref>

<ref name=Kunen1980_171>
{{Cite book
 |last=Kunen  |first=Kenneth  |author-link=Kenneth Kunen
 |year=1980
 |title=[[Set Theory: An Introduction to Independence Proofs]]
 |page=171
 |location=Amsterdam, NL
 |publisher=North-Holland
 |isbn=978-0-444-85401-8
}}
</ref>

<ref name=Freiling1986>
{{Cite journal
 |last=Freiling |first=Chris
 |year=1986
 |title=Axioms of Symmetry: Throwing darts at the real number line
 |journal=Journal of Symbolic Logic
 |volume=51  |issue=1  |pages=190–200
 |publisher=Association for Symbolic Logic
 |doi=10.2307/2273955 |jstor=2273955
|s2cid=38174418
 }}
</ref>

<ref name=Foreman2003>
{{Cite web
 |last=Foreman |first=Matt
 |year=2003
 |title=Has the Continuum Hypothesis been settled?
 |access-date=25 February 2006
 |url=http://www.math.helsinki.fi/logic/LC2003/presentations/foreman.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://www.math.helsinki.fi/logic/LC2003/presentations/foreman.pdf |archive-date=2022-10-10 |url-status=live
}}
</ref>

<ref name=Feferman2011>
{{Cite web
 |last=Feferman |first=Solomon |author-link=Solomon Feferman
 |year=2011
 |title=Is the Continuum Hypothesis a definite mathematical problem?
 |work=Exploring the Frontiers of Independence
 |series=Harvard lecture series 
 |url=http://math.stanford.edu/~feferman/papers/IsCHdefinite.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://math.stanford.edu/~feferman/papers/IsCHdefinite.pdf |archive-date=2022-10-10 |url-status=live
}}
</ref>

<ref name=Hamkins2012>
{{Cite journal
 |last=Hamkins |first=Joel David  |author-link=Joel David Hamkins
 |year=2012
 |title=The set-theoretic multiverse
 |journal=The Review of Symbolic Logic
 |volume=5 |issue=3 |pages=416–449
|doi=10.1017/S1755020311000359 |s2cid=33807508 |arxiv=1108.4223}}
</ref>

<ref name=Hamkins2015>{{cite journal
 | last = Hamkins | first = Joel David
 | date = January 2015
 | doi = 10.1215/00294527-2835047
 | issue = 1
 | journal = Notre Dame Journal of Formal Logic
 | title = Is the Dream Solution of the Continuum Hypothesis Attainable?
 | volume = 56| arxiv = 1203.4026
 }}</ref>

<ref name=Shelah2003>
{{Cite journal
 |last=Shelah |first=Saharon
 |year=2003
 |title=Logical dreams
 |journal=Bulletin of the American Mathematical Society |series=New Series
 |volume=40 |issue=2 |pages=203–228
 |doi=10.1090/s0273-0979-03-00981-9
 |arxiv=math/0211398
|s2cid=1510438
 }}
</ref>

<ref name=Jourdain1905>
{{Cite journal
 |last=Jourdain |first=Philip E.B.
 |year=1905
 |title=On transfinite cardinal numbers of the exponential form
 |journal=Philosophical Magazine
 |series=Series&nbsp;6
 |volume=9  |issue=49
 |pages=42–56
 |doi=10.1080/14786440509463254
 |url=https://www.biodiversitylibrary.org/page/39515382
}}
</ref>

<ref name=Moore2011>
{{Cite journal
 |last=Moore  |first=Gregory H.
 |year=2011
 |title=Early history of the generalized continuum hypothesis: 1878–1938
 |journal=Bulletin of Symbolic Logic
 |volume=17  |issue=4  |pages=489–532
 |doi=10.2178/bsl/1318855631
 |mr=2896574
}}
</ref>

<ref name=Gillman2002>
{{Cite journal
 |last=Gillman  |first=Leonard
 |year=2002
 |title=Two classical surprises concerning the Axiom of Choice and the Continuum Hypothesis
 |journal=American Mathematical Monthly
 |volume=109  |issue=6
 |pages=544–553
 |doi=10.2307/2695444
 |jstor=2695444
 |url=http://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gillman544-553.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gillman544-553.pdf |archive-date=2022-10-10 |url-status=live
}}
</ref>

<ref name=Merimovich2007>
{{cite journal
 |last=Merimovich |first=Carmi
 |year=2007
 |title=A power function with a fixed finite gap everywhere
 |journal=[[Journal of Symbolic Logic]]
 |volume=72  |issue=2  |pages=361–417
 |doi=10.2178/jsl/1185803615
 |mr=2320282  |arxiv=math/0005179
|s2cid=15577499
 }}
</ref>

<ref name=Patai1930>
{{Cite journal
 |last=Patai |first=L.
 |year=1930
 |title=Untersuchungen über die א-reihe
 |journal=Mathematische und naturwissenschaftliche Berichte aus Ungarn
 |volume=37  |pages=127–142
 |language=de
}}
</ref>

<ref name=HaydenKennison1968>
{{Cite book
 |last1=Hayden   |first1=Seymour
 |last2=Kennison |first2=John F.
 |year=1968
 |title=Zermelo-Fraenkel Set Theory
 |location=Columbus, Ohio
 |publisher=Charles E. Merrill 
 |page=147, exercise&nbsp;76
}}
</ref>

}} <!-- end "refs=" -->

* {{Cite journal
 |last=Maddy |first=Penelope
 |date=June 1988
 |title=Believing the axioms, [part&nbsp;I]
 |journal=Journal of Symbolic Logic
 |volume=53  |issue=2  |pages=481–511
 |publisher=Association for Symbolic Logic
 |doi=10.2307/2274520 |jstor=2274520
}}