Editing Mathematical logic (section)

=== Classical papers, texts, and collections ===
* {{cite journal |last1=Banach |first1=Stefan |author-link1=Stefan Banach |last2=Tarski |first2=Alfred |author-link2=Alfred Tarski |date=1924 |title=Sur la décomposition des ensembles de points en parties respectivement congruentes |journal=[[Fundamenta Mathematicae]] |volume=6 |pages=244–277 |doi=10.4064/fm-6-1-244-277 |language=fr |doi-access=free |url=http://matwbn.icm.edu.pl/ksiazki/fm/fm6/fm6127.pdf
}}
{{cite book |editor-last=Bochenski |editor-first=Jozef Maria |date=1959 |translator=Otto Bird |title=A Precis of Mathematical Logic |series=Synthese Library, Vol. 1 |location=[[Dordrecht]] |publisher=[[Springer Science+Business Media|Springer]] |doi=10.1007/978-94-017-0592-9 |isbn=9789048183296 
}}
*{{Cite book |last=Burali-Forti |first=Cesare |date=1897 |title=A question on transfinite numbers }} Reprinted in {{harvnb|van Heijenoort|1976|pp=104–111
}}
{{Cite journal |last=Cantor |first=Georg |year=1874 |title=Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen |journal=[[Journal für die Reine und Angewandte Mathematik]] |volume=1874 |issue=77 |pages=258–262 |doi=10.1515/crll.1874.77.258 |s2cid=199545885 |url=http://gdz.sub.uni-goettingen.de/download/PPN243919689_0077/PPN243919689_0077___LOG_0014.pdf 
}}
{{cite book |last=Carroll |first=Lewis |author-link=Lewis Carroll |date=1896 |title=Symbolic Logic |publisher=Kessinger Legacy Reprints |isbn=9781163444955 |url=https://www.gutenberg.org/ebooks/28696
}}
*{{cite book |last=Dedekind |first=Richard |author-link=Richard Dedekind |date=1872 |title=Stetigkeit und irrationale Zahlen |language=de  }} English translation as: "Consistency and irrational numbers".
*{{cite book |last=Dedekind |first=Richard |author-link=Richard Dedekind |date=1888 |title=Was sind und was sollen die Zahlen? }} Two English translations:
**1963 (1901). ''Essays on the Theory of Numbers''. Beman, W. W., ed. and trans. Dover.
**1996. In ''From Kant to Hilbert: A Source Book in the Foundations of Mathematics'', 2 vols, Ewald, William B., ed., [[Oxford University Press]]: 787–832.
*{{cite book |last1=Fraenkel |first1=Abraham A. |author1-link=Abraham Fraenkel |date=1922 |contribution=Der Begriff 'definit' und die Unabhängigkeit des Auswahlsaxioms |title=Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse |pages=253–257 |language=de }} Reprinted in English translation as "The notion of 'definite' and the independence of the axiom of choice" in {{harvnb|van Heijenoort|1976|pp=284–289}}.
* [[Gottlob Frege|Frege, Gottlob]] (1879), ''[[Begriffsschrift]], eine der arithmetischen nachgebildete Formelsprache des reinen Denkens''. Halle a. S.: Louis Nebert. Translation: ''Concept Script, a formal language of pure thought modelled upon that of arithmetic'', by S. Bauer-Mengelberg in {{harvnb|van Heijenoort|1976}}.
* [[Gottlob Frege|Frege, Gottlob]] (1884), ''Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl''. Breslau: W. Koebner. Translation: [[J. L. Austin]], 1974. ''The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number'', 2nd ed. Blackwell.
* {{cite journal |last=Gentzen |first=Gerhard |author-link=Gerhard Gentzen |date=1936 |title=Die Widerspruchsfreiheit der reinen Zahlentheorie |journal=Mathematische Annalen |volume=112 |pages=132–213 |doi=10.1007/BF01565428 |s2cid=122719892  }} Reprinted in English translation in Gentzen's ''Collected works'', M. E. Szabo, ed., North-Holland, Amsterdam, 1969.
*{{Cite book |last=Gödel |first=Kurt |author-link=Kurt Gödel |date=1929 |title=Über die Vollständigkeit des Logikkalküls |trans-title=Completeness of the logical calculus |series=doctoral dissertation |publisher=University Of Vienna
}}
* {{Cite journal |last=Gödel |first=Kurt |author-link=Kurt Gödel |date=1930 |title=Die Vollständigkeit der Axiome des logischen Funktionen-kalküls |trans-title=The completeness of the axioms of the calculus of logical functions |journal= Monatshefte für Mathematik und Physik |volume=37 |pages=349–360 |doi=10.1007/BF01696781 |s2cid=123343522 |language=de
}}
* {{Cite journal |last=Gödel |first=Kurt |author-link=Kurt Gödel |date=1931 |title=Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I |trans-title=[[On Formally Undecidable Propositions of Principia Mathematica and Related Systems]] |journal=Monatshefte für Mathematik und Physik |volume=38 |issue=1 |pages=173–198 |doi=10.1007/BF01700692 |s2cid=197663120 |language=de }}
*{{Cite journal |last=Gödel |first=Kurt |author-link=Kurt Gödel |date=1958 |title=Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes |journal=Dialectica |volume=12 |issue=3–4 |pages=280–287 |doi=10.1111/j.1746-8361.1958.tb01464.x |doi-access=free |language=de }} Reprinted in English translation in Gödel's ''Collected Works'', vol II, [[Solomon Feferman]] et al., eds. Oxford University Press, 1993.
* {{cite book |editor-last=van Heijenoort |editor-first=Jean |editor-link=Jean van Heijenoort |date=1976 |orig-date=1967 |title=From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 |edition=3rd |location=[[Cambridge, Massachusetts|Cambridge MA]] |publisher=[[Harvard University Press]] |isbn=9780674324497 |id=(pbk.) 
}}
*{{cite book |last=Hilbert |first=David |author-link=David Hilbert |date=1899 |title=Grundlagen der Geometrie |location=[[Leipzig]] |publisher=Teubner |language=de}} English 1902 edition (''The Foundations of Geometry'') republished 1980, Open Court, Chicago.
*{{Cite journal |last=Hilbert |first=David |author-link=David Hilbert |date=1929 |title=Probleme der Grundlegung der Mathematik |journal=Mathematische Annalen |volume=102 |pages=1–9 |doi=10.1007/BF01782335 |s2cid=122870563 |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002273500&L=1 }} Lecture given at the International Congress of Mathematicians, 3 September 1928. Published in English translation as "The Grounding of Elementary Number Theory", in Mancosu 1998, pp.&nbsp;266–273.
* {{Cite book |last1=Hilbert |first1=David |author1-link=David Hilbert |last2=Bernays |first2=Paul |author2-link=Paul Bernays |date=1934 |title=Grundlagen der Mathematik. I |series=Die Grundlehren der mathematischen Wissenschaften |volume=40 |location=Berlin, New York City |publisher=[[Springer Science+Business Media|Springer]] |isbn=9783540041344 |mr=0237246 |jfm=60.0017.02
}}
* {{Cite journal |last=Kleene |first=Stephen Cole |author-link=Stephen Kleene |date=1943 |title=Recursive Predicates and Quantifiers |journal= Transactions of the American Mathematical Society|volume=53 |issue=1 |pages=41–73 |doi=10.2307/1990131 |jstor=1990131 |doi-access=free
}}
* {{Cite book |last=Lobachevsky |first=Nikolai |author-link=Nikolai Lobachevsky |date=1840 |title=Geometrishe Untersuchungen zur Theorie der Parellellinien |language=de }} Reprinted in English translation as {{cite book |date=1955 |chapter=Geometric Investigations on the Theory of Parallel Lines |editor=Robert Bonola |title=Non-Euclidean Geometry |publisher=Dover |isbn=0-486-60027-0
}}
* {{Cite journal |last1=Löwenheim |first1=Leopold |author1-link=Leopold Löwenheim |date=1915 |title=Über Möglichkeiten im Relativkalkül |journal=Mathematische Annalen |volume=76 |issue=4 |pages=447–470 |doi=10.1007/BF01458217 |issn=0025-5831 |s2cid=116581304 |language=de |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002266121&L=1 }} Translated as "On possibilities in the calculus of relatives" in {{cite book |author=Jean van Heijenoort |author-link=Jean van Heijenoort |date=1967 |title=A Source Book in Mathematical Logic, 1879–1931 |publisher=Harvard Univ. Press |pages=228–251
}}
*{{Cite book |editor-last=Mancosu |editor-first=Paolo |editor-link=Paolo Mancosu |date=1998 |title=From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s |publisher=Oxford University Press
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*{{cite book |last=Pasch |first=Moritz |author-link=Moritz Pasch |date=1882 |title=Vorlesungen über neuere Geometrie
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*{{cite book |last=Peano |first=Giuseppe |author-link=Giuseppe Peano |date=1889 |title=Arithmetices principia, nova methodo exposita |title-link=Arithmetices principia, nova methodo exposita |language=lt }} Excerpt reprinted in English translation as "The principles of arithmetic, presented by a new method"in {{harvnb|van Heijenoort|1976|pp=83–97}}.
* {{Cite journal |last=Richard |first=Jules |date=1905 |title=Les principes des mathématiques et le problème des ensembles |journal=Revue Générale des Sciences Pures et Appliquées |volume=16 |page=541 |language=fr}} Reprinted in English translation as "The principles of mathematics and the problems of sets" in {{harvnb|van Heijenoort|1976|pp=142–144}}.
* {{Cite journal |last1=Skolem |first1=Thoralf |author1-link=Thoralf Skolem |date=1920 |title=Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen |journal=Videnskapsselskapet Skrifter, I. Matematisk-naturvidenskabelig Klasse |volume=6 |pages=1–36 |language=de
}}
{{cite web |last=Soare |first=Robert Irving |date=22 December 2011 |title=Computability Theory and Applications: The Art of Classical Computability |website=Department of Mathematics |publisher=University of Chicago |access-date=23 August 2017 |url=http://www.people.cs.uchicago.edu/~soare/Turing/frontice.pdf
}}
{{cite book |last=Swineshead |first=Richard |author-link=Richard Swineshead |date=1498 |title=Calculationes Suiseth Anglici |publisher=Papie: Per Franciscum Gyrardengum |language=lt 
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* {{Cite book |last=Tarski |first=Alfred |author-link=Alfred Tarski |date=1948 |title=A decision method for elementary algebra and geometry |location=[[Santa Monica, California|Santa Monica CA]] |publisher=[[RAND Corporation]]
}}
*{{Cite journal |last1=Turing |first1=Alan M. |author1-link=A. M. Turing |date=1939 |title=Systems of Logic Based on Ordinals |journal=[[Proceedings of the London Mathematical Society]] |volume=45 |issue=2 |pages=161–228 |doi=10.1112/plms/s2-45.1.161 |hdl=21.11116/0000-0001-91CE-3 |hdl-access=free
}}
* {{cite book |last=Weyl |first=Hermann |date=1918 |title=Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis |location=Leipzig |language=de
}}
* {{Cite journal |last=Zermelo |first=Ernst |author-link=Ernst Zermelo |date=1904 |title=Beweis, daß jede Menge wohlgeordnet werden kann |journal=Mathematische Annalen |volume=59 |issue=4 |pages=514–516 |doi=10.1007/BF01445300 |s2cid=124189935 |language=de |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002260018&L=1 }} Reprinted in English translation as "Proof that every set can be well-ordered" in {{harvnb|van Heijenoort|1976|pp=139–141}}.
* {{Cite journal |last=Zermelo |first=Ernst |author-link=Ernst Zermelo |date=1908a |title=Neuer Beweis für die Möglichkeit einer Wohlordnung |journal=[[Mathematische Annalen]] |volume=65 |pages=107–128 |doi=10.1007/BF01450054 |issn=0025-5831 |s2cid=119924143 |language=de |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002261952&L=1 }} Reprinted in English translation as "A new proof of the possibility of a well-ordering" in {{harvnb|van Heijenoort|1976|pp=183–198}}.
* {{Cite journal |last=Zermelo |first=Ernst |author-link=Ernst Zermelo |date=1908b |title=Untersuchungen über die Grundlagen der Mengenlehre |journal=Mathematische Annalen |volume=65 |issue=2 |pages=261–281 |doi=10.1007/BF01449999 |s2cid=120085563 |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0065&DMDID=DMDLOG_0018&L=1 }}