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==Selected publications== * 1935. {{cite journal |url=https://www.jstor.org/stable/2372027 |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene|display-authors=0|title=A Theory of Positive Integers in Formal Logic. Part I |journal=[[American Journal of Mathematics]]|volume=57 |number=1 |pages=153β173 |date=Jan 1935 |doi=10.2307/2372027 |jstor=2372027}} * 1935. {{cite journal |url=https://www.jstor.org/stable/2371199 |author-first=Stephen Cole|author-last=Kleene |author-link=Stephen Cole Kleene|display-authors=0|title=A Theory of Positive Integers in Formal Logic. Part II |journal=American Journal of Mathematics |volume=57 |number=2 |pages=219β244 |date=Apr 1935 |doi=10.2307/2371199 |jstor=2371199}} * 1935. {{cite journal |jstor=1968646 |author-first1=Stephen Cole|author-last1=Kleene |author-link1=Stephen Cole Kleene|author-first2=J. Barkley|author-last2=Rosser|author-link2=J. Barkley Rosser|author-mask=1|title=The Inconsistency of Certain Formal Logics |journal=Annals of Mathematics |series=2nd Series |volume=36 |number=3 |pages=630β636 |date=Jul 1935 |doi=10.2307/1968646}} * 1936. {{cite journal |title=General recursive functions of natural numbers |journal=[[Mathematische Annalen]] |issue=112 |pages=727β742 |date=1936 |url=http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002278499}} * 1936. {{cite journal |url=https://projecteuclid.org/euclid.dmj/1077489488 |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene|author-mask=0 |title=<math>\lambda</math>-definability and recursiveness |journal=Duke Mathematical Journal |volume=2 |number=2 |pages=340β352 |year=1936}} * 1938. {{cite journal |url=http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Kleene%20-%20Ordinals.pdf |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene|author-mask=0 |title=On Notations for Ordinal Numbers |journal=Journal of Symbolic Logic |volume=3 |pages=150β155 |year=1938 |issue=4 |doi=10.2307/2267778 |jstor=2267778|s2cid=34314018 }} * 1943. {{cite journal |doi=10.1090/S0002-9947-1943-0007371-8 |url=https://www.ams.org/journals/tran/1943-053-01/S0002-9947-1943-0007371-8/ |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene |author-mask=0 |title=Recursive predicates and quantifiers |journal=Transactions of the American Mathematical Society |volume=53 |number=1 |pages=41β73 |date=Jan 1943 |doi-access=free}} * 1951. {{cite news |title=Representation of Events in Nerve Nets and Finite Automata |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene |display-authors=0|date=15 December 1951 |series=U. S. Air Force Project Rand Research Memorandum |number=RM-704 |url=https://www.rand.org/content/dam/rand/pubs/research_memoranda/2008/RM704.pdf |publisher=[[The RAND Corporation]]}} * 1952. {{Cite book |last=Kleene |first=Stephen Cole |author-link=Stephen Cole Kleene |display-authors=0 |title=Introduction to Metamathematics |publisher=Van Nostrand|location=New York |year=1952 |oclc=523942 }}<ref>{{Cite book|last=Kleene|first=Stephen Cole|author-link=Stephen Cole Kleene|display-authors=0|title=reprint|publisher= [[Ishi Press]]|orig-year=1952|date=13 March 2009|isbn=9780923891572}}</ref> * 1956. {{cite book |chapter=Representation of Events in Nerve Nets and Finite Automata |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene |display-authors=0|title=Automata Studies |editor-first1=Claude |editor-last1=Shannon |editor-link1=Claude Shannon |editor-first2=John |editor-last2=McCarthy |editor-link2=John McCarthy (computer scientist) |oclc=564148 |date=1956}} * 1965 {{Cite book |last1=Kleene |first1=Stephen Cole |author-link1=Stephen Cole Kleene |author-last2=Vesley |author-first2=Richard Eugene |author-mask=1 |title=The Foundations of Intuitionistic Mathematics |publisher=North-Holland }}<ref>{{cite journal|author-last=Bishop|author-first=Errett|author-link=Errett Bishop |title=Review: The foundations of intuitionistic mathematics|journal=[[Bulletin of the American Mathematical Society]] |date=1965 |volume=71 |issue=6 |pages=850β852 |url=https://www.ams.org/journals/bull/1965-71-06/S0002-9904-1965-11412-4/S0002-9904-1965-11412-4.pdf |doi=10.1090/s0002-9904-1965-11412-4 |doi-access=free}}</ref> * 1967. ''[https://www.worldcat.org/oclc/523472 Mathematical Logic.]'' [[John Wiley & Sons]]. Dover reprint, 2002. {{ISBN|0-486-42533-9}}. * 1981. "Origins of Recursive Function Theory" in ''[https://www.worldcat.org/oclc/4583089 Annals of the History of Computing 3],'' No. 1. * 1987. {{cite journal |author-first=Stephen Cole |author-last=Kleene |author-link=Stephen Cole Kleene|author-mask=0 |title=Reflections on Church's thesis |journal=Notre Dame Journal of Formal Logic |volume=28 |number=4 |pages=490β498 |date=Oct 1987 |doi=10.1305/ndjfl/1093637645 |doi-access=free}}
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