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Gödel's incompleteness theorems
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=== Articles by others === * {{cite journal |last=Boolos |first=George|author-link=George Boolos|title=A New Proof of the Gödel Incompleteness Theorem|year=1989 |journal=[[Notices of the American Mathematical Society]]|volume=36|pages=388–390, 676|quote=reprinted in {{harvtxt|Boolos|1998|pages=383–388}}}} * {{cite book |last=Boolos |first=George|author-link=George Boolos|title=Logic, logic, and logic|year=1998|publisher=[[Harvard University Press]]|isbn=0-674-53766-1|pages=443}} * Bernd Buldt, 2014, "[http://opus.ipfw.edu/cgi/viewcontent.cgi?article=1297&context=philos_facpubs The Scope of Gödel's First Incompleteness Theorem] {{Webarchive|url=https://web.archive.org/web/20160306110140/http://opus.ipfw.edu/cgi/viewcontent.cgi?article=1297&context=philos_facpubs |date=2016-03-06 }}", ''[[Logica Universalis]]'', v. 8, pp. 499–552. {{doi|10.1007/s11787-014-0107-3}} * {{cite journal |last1=Charlesworth |first1=Arthur |title=A Proof of Godel's Theorem in Terms of Computer Programs |journal=Mathematics Magazine |date=1981 |volume=54 |issue=3 |pages=109–121 |doi=10.2307/2689794 |jstor=2689794}} * {{cite book |last1=Davis |first1=Martin |title=The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions |date=1965 |publisher=Raven Press |isbn=978-0-911216-01-1 |url=https://books.google.com/books?id=euBQAAAAMAAJ |language=en}} * {{cite journal |author-link=Martin Davis (mathematician) |first=Martin |last=Davis |date=2006 |url=https://www.ams.org/notices/200604/fea-davis.pdf |title=The Incompleteness Theorem |journal=Notices of the AMS |volume=53 |issue=4 |page=414}} * {{cite journal|url=http://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002369001|title=Formale Beweise und die Entscheidbarkeit|journal=Mathematische Zeitschrift |year=1926 |volume=25 |pages=676–682 |doi=10.1007/bf01283861 |last1=Finsler|first1=Paul|s2cid=121054124}} * {{cite book |editor-last=Grattan-Guinness |editor-first=Ivor |editor-link=Ivor Grattan-Guinness |title=Landmark Writings in Western Mathematics 1640-1940 |publisher=Elsevier |isbn=9780444508713 |date=2005}} * {{cite book |author-link=Jean van Heijenoort |first=Jean |last=van Heijenoort |date=1967 |chapter=Gödel's Theorem |editor=Edwards, Paul |title=[[The Encyclopedia of Philosophy|Encyclopedia of Philosophy]] |volume=3 |publisher=Macmillan |pages=348–357}} * {{cite journal |author-link=Geoffrey Hellman |first=Geoffrey |last=Hellman |date=1981 |title=How to Gödel a Frege-Russell: Gödel's Incompleteness Theorems and Logicism |journal=Noûs |volume=15 |issue=4 - Special Issue on Philosophy of Mathematics |pages=451–468 |doi=10.2307/2214847 |jstor=2214847 |issn=0029-4624}} * [[David Hilbert]], 1900, "[http://aleph0.clarku.edu/~djoyce/hilbert/problems.html#prob2 Mathematical Problems.]" English translation of a lecture delivered before the International Congress of Mathematicians at Paris, containing Hilbert's statement of his Second Problem. * Martin Hirzel, 2000, "[https://web.archive.org/web/20040916041216/http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf On formally undecidable propositions of Principia Mathematica and related systems I.]." An English translation of Gödel's paper. Archived from [http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf the original]. Sept. 16, 2004. * {{cite journal |last1=Kikuchi |first1=Makoto |last2=Tanaka |first2=Kazuyuki |title=On Formalization of Model-Theoretic Proofs of Gödel's Theorems |journal=Notre Dame Journal of Formal Logic |date=July 1994 |volume=35 |issue=3 |pages=403–412 |doi=10.1305/ndjfl/1040511346 |mr=1326122|doi-access=free }} * {{cite journal |last1=Kleene |first1=S. C. |author-link1=Stephen Cole Kleene |title=Recursive predicates and quantifiers |journal=Transactions of the American Mathematical Society |date=1943 |volume=53 |issue=1 |pages=41–73 |doi=10.1090/S0002-9947-1943-0007371-8}} Reprinted in {{harvnb|Davis|1965|pp=255–287}} * {{cite web |first=Panu |last=Raatikainen |date=2020 |url=https://plato.stanford.edu/entries/goedel-incompleteness/ |title=Gödel's Incompleteness Theorems |publisher=Stanford Encyclopedia of Philosophy |access-date=November 7, 2022}} * {{cite journal |first=Panu |last=Raatikainen |date=2005 |url=https://www.cairn.info/revue-internationale-de-philosophie-2005-4-page-513.htm |title=On the philosophical relevance of Gödel's incompleteness theorems |journal=Revue Internationale de Philosophie |volume=59 |issue=4 |pages=513–534|doi=10.3917/rip.234.0513 |s2cid=52083793 }} * [[John Barkley Rosser]], 1936, "Extensions of some theorems of Gödel and Church", reprinted from the ''Journal of Symbolic Logic'', v. 1 (1936) pp. 87–91, in Martin Davis 1965, ''The Undecidable'' (loc. cit.) pp. 230–235. * —, 1939, "An Informal Exposition of proofs of Gödel's Theorem and Church's Theorem", Reprinted from the ''Journal of Symbolic Logic'', v. 4 (1939) pp. 53–60, in Martin Davis 1965, ''The Undecidable'' (loc. cit.) pp. 223–230 * {{cite book |last=Smoryński |first=C. |chapter=The incompleteness theorems |editor=[[Jon Barwise]] |title=Handbook of mathematical logic |date=1977 |publisher=North-Holland Pub. Co |location=Amsterdam |isbn=978-0-444-86388-1 |pages=821–866}} * {{cite journal |last=Willard |first=Dan E. |year=2001 |title=Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles |journal=Journal of Symbolic Logic |volume=66 |number=2 |pages=536–596 |doi=10.2307/2695030 |jstor=2695030}} * {{cite journal | last=Zach | first=Richard |author-link=Richard Zach | year=2003 | title=The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program | journal=[[Synthese]] | publisher=Springer Science and Business Media LLC | volume=137 | issue=1 |issn=0039-7857 | doi=10.1023/a:1026247421383 | pages=211–259 |url=http://people.ucalgary.ca/~rzach/static/conprf.pdf| arxiv=math/0102189 | s2cid=16657040 }} * {{cite book | last=Zach | first=Richard |author-link=Richard Zach | year=2005 | chapter=Kurt Gödel, paper on the incompleteness theorems (1931) |pages=917–925 |editor-last=Grattan-Guinness |editor-first=Ivor |editor-link=Ivor Grattan-Guinness | title=Landmark Writings in Western Mathematics 1640-1940| publisher=Elsevier | doi=10.1016/b978-044450871-3/50152-2| isbn=9780444508713 | url=https://philarchive.org/rec/ZACKGP }}
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