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Topic: Stephen Kleene

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Stephen Cole Kleene

Kleene closure

Intuitionistic logic

Alonzo Church

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Mathematical intuitionism

Completed infinity

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	Stephen Cole Kleene (Site not responding. Last check: 2007-10-07)
		Stephen Cole Kleene (pronounced "KLAY-nee") was born on January 5, 1909 in Hartford, Connecticut.
		Steve Kleene was one of the pioneers of 20th century mathematics.
		In 1990 Kleene was awarded the President's National Medal of Science, the country's highest scientific honor, for his leadership in the theory of recursion and effective computability and for developing it into a deep and broad field of mathematical research.
	www.library.wisc.edu /libraries/Math/kleene.htm (552 words)

	Stephen Cole Kleene, January 5, 1909—January 25, 1994 \| By Saunders Mac Lane \| Biographical Memoirs
		Kleene and his fellow student Barkley Rosser studied it with care, and presently found that it led to a contradiction.
		Kleene combined those ideas with notes of von Neumann on automata to produce a RAND report that has been very influential in the study of automata.
		Kleene was elected to membership in the National Academy of Sciences in 1969.
	www.nap.edu /html/biomems/skleene.html (1566 words)

	Stephen Kleene - Computing Reference - eLook.org
		Kleene was best known for founding the branch of mathematical logic known as recursion theory and for inventing regular expressions.
		The Kleene star and Ascending Kleene Chain are named after him.
		His son, Ken Kleene , wrote: "As far as I am aware this pronunciation is incorrect in all known languages.
	www.elook.org /computing/stephen-kleene.htm (330 words)

	Stephen Kleene (Site not responding. Last check: 2007-10-07)
		Stephen Cole Kleene (January 5, 1909 - January 25, 1994) wasan American mathematician whose work at the University of Wisconsin - Madison helped lay the foundations for theoretical computer science.
		Byproviding methods of determining which problems are solvable, Kleene's work led to the study of which functions are computable.
		He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C. In 1946, he returned to Wisconsin,becoming a full professor in 1948.
	www.therfcc.org /stephen-kleene-65487.html (408 words)

	Kleene (Site not responding. Last check: 2007-10-07)
		Kleene's research was on the theory of algorithms and recursive functions.
		Kleene's formulation of computable function via six schemata is one of the most succinct and useful, and his previous work on lambda functions played a major role in supporting Church's Thesis that these classes coincide with the intuitively calculable functions.
		Kleene developed a diverse array of topics in computability: the arithmetical hierarchy, degrees of computability, computable ordinals and hyperarithmetic theory, finite automata and regular sets with enormous consequences for computer science, computability on higher types, recursive realizability for intuitionistic arithmetic with consequences for philosphy and for program correctness in computer science.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Kleene.html (338 words)

	UW Math PhD Alumni (Advisor: Kleene)
		Stephen Cole Kleene was born on January 5, 1909 in Hartford, Connecticut.
		Kleene first came to Madison in 1935 as an instructor and in 1937 was promoted to assistant professor.
		In 1990 Steve Kleene won the National medal of Science, the country's highest scientific honor, for his leadership in the theory of recursion and effective computability and for developing it into a deep and broad field of mathematical research.
	www.math.wisc.edu /directories/alumni/bio-kleene.htm (442 words)

	STEPHEN KLEENE (Site not responding. Last check: 2007-10-07)
		Professor Stephen Cole Kleene (1909-01-05 - 1994-01-26) /steev'n (kohl) klay'nee/ An American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for modern computer science.
		He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C. In 1946, he returned to Wisconsin, eventually becoming a full professor.
		Specialty definitions using "STEPHEN KLEENE": Kleene star, Kleene, Stephen Cole ♦ Stephen Cole Kleene.
	www.websters-online-dictionary.org /St/Stephen+Kleene.html (465 words)

	Stephen Cole Kleene
		Kleene begründete die nach ihm und Mostowski benannte Hierarchie der arithmetischen Mengen und behandelte Probleme der klassischen Interpretation der intuitionistischen Logik und Mathematik.
		Bei Kleene steht der dritte Wahrheitswert dabei für undefiniert.
		In der Automatentheorie entwickelte Kleene den Kalkül der regulären Ereignisse.
	www.philosophenlexikon.de /kleene.htm (172 words)

	Stephen Cole Kleene -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		By providing methods of determining which problems are solvable, Kleene's work led to the study of which functions are (Click link for more info and facts about computable function) computable function.
		The (Click link for more info and facts about Kleene star) Kleene star, (Click link for more info and facts about Kleene's recursion theorem) Kleene's recursion theorem and the Ascending Kleene Chain are named after him.
		Kleene was born in (The state capital of Connecticut; located in central Connecticut on the Connecticut river; a center of the insurance business) Hartford, (A New England state; one of the original 13 colonies) Connecticut, (The army of the United States of America; organizes and trains soldiers for land warfare) USA.
	www.absoluteastronomy.com /encyclopedia/s/st/stephen_cole_kleene.htm (490 words)

	Stephen Cole Kleene (Site not responding. Last check: 2007-10-07)
		Stephen Cole Kleene (de enero el 5 de 1909 - de enero el 25 de 1994) era un trabajo del matemático americano que en la universidad de Wisconsin-Madison ayudada para descansar las fundaciones para la informática teórica.
		Kleene era el mejor conocido para fundar el sucursal de la lógica matemática conocido como teoría de la repetición junto con la iglesia de Alonzo, Kurt Gödel, Alan Turing y otros; y para inventar expresiones regulares.
		Kleene pronunció su nombre pasado/klay'nee/./klee'nee/y/kleen los mispronunciations extremadamente comunes de /.are.
	www.yotor.net /wiki/es/st/Stephen%20Cole%20Kleene.htm (521 words)

	Read about Stephen Cole Kleene at WorldVillage Encyclopedia. Research Stephen Cole Kleene and learn about Stephen Cole ... (Site not responding. Last check: 2007-10-07)
		Kleene was best known for founding the branch of
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to
		An avid mountain climber, Kleene had a strong interest in nature and the
	encyclopedia.worldvillage.com /s/b/Stephen_Kleene (398 words)

	Nat' Academies Press, Biographical Memoirs V.75 (1998)
		And Kleene examined the more general recursive functions used by Gödel. Church advanced the speculative thesis that the effectively computable functions (of numbers) could be identified with the λ-definable func-
		Much of Kleene's subsequent work was devoted to the systematic study of this class of recursive (computable) functions, as well represented in his magnificent 1952 book Introduction to Metamathematics and his treatment of the partial recursive functions—those defined recursively, but only for some numbers, hence partial.
		(This was a comeback; when Kleene left Wisconsin for Amherst in 1941, the dean of the college had declined to promote him, but he had assured Kleene that he would return.) His wife Nancy died in 1970.
	books.nap.edu /books/0309062950/html/154.html (1889 words)

	Stephen Cole Kleene: Definition and Links by Encyclopedian.com - All about Stephen Cole Kleene (Site not responding. Last check: 2007-10-07)
		Stephen Cole Kleene: Definition and Links by Encyclopedian.com - All about Stephen Cole Kleene
		Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin - Madison helped lay the foundations for theoretical computer science.
		By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions are computable.
	www.encyclopedian.com /st/Stephen-Kleene.html (414 words)

	Citations: Introduction to Metamathematics - Kleene (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		....Kleene s three valued logic [26, 24, 44] We require that #R#(a1, a i, a i 2, ak) undef for every relational symbol R. Logical connectives in Kleene s strong threevalued logic are the strongest regular extension of the corresponding connectives on the two valued domain
		Stephen Cole Kleene was the mathematician who saw most deeply into the nature of intuitionism, with his notion of recursive realizabilility; see [4] and
		I shall discuss realizability for formulas of arithmetic; the modifications necessary to discuss the free word algebra W are minor; for example, induction for W should be formulated as A x (ffl) 8x[A A x (0x) A x (1x) A: The function symbols are 0, S (successor) and Delta.
	citeseer.ist.psu.edu /context/169070/0 (1750 words)

	Kleene, Stephen Cole -- Encyclopædia Britannica
		Kleene was educated at Amherst College (A.B., 1930) and earned a Ph.D. in mathematics at Princeton University in 1934.
		The character of Stephen Dedalus appears in two works by Irish author James Joyce—the autobiographical novel A Portrait of the Artist as a Young Man (1916) and Ulysses (1922).
		The English critic and man of letters Leslie Stephen was the first editor of the Dictionary of National Biography.
	www.britannica.com /eb/article-9001456?tocId=9001456 (725 words)

	Stephen Kleene (Site not responding. Last check: 2007-10-07)
		In a 1956 paper, Kleene introduced the notion of regular expression, and proved that the languages specified by regular expressions and the languages generated by finite automata constituted the same class, a basic result today known as Kleene's Theorem.
		Kleene wrote two books, one of which was Introduction to Metamathematics (North-Holland, 1952).
		Kleene died in Madison, Wisconsin on January 25, 1994.
	www.student.cs.uwaterloo.ca /~cs462/Hall/kleene.html (144 words)

	Stephen Cole Kleene Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-07)
		Looking For stephen cole kleene - Find stephen cole kleene and more at Lycos Search.
		Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science.
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to Gödeliness" among logicians (a pun on "Cleanliness is next to godliness").
	www.karr.net /search/encyclopedia/Stephen_Cole_Kleene (656 words)

	Mathematical Logic by Stephen Cole Kleene (Site not responding. Last check: 2007-10-07)
		Kleene is brilliant and painstakingly accurate--sometimes I forget he is human.
		Wishing recently to refresh my (extremely rusty) memories of the propositional calculus and the first-order predicate calculus, I picked up this meaty text and was extremely dismayed to find myself soundly defeated within the first few pages.
		Kleene does not even make a pretense of holding the reader's hand: either you get it or you don't.
	www.internetcross.com /item/0486425339 (369 words)

	Stephen Cole Kleene - Hotel Resource Book Store (Site not responding. Last check: 2007-10-07)
		It certainly is introductory since the basics of both propositional and predicate logic, and formal...
		This is one of those books that don't get old; although it was first published in 1952, and since then much has been made in Mathematical Logic, Kleene's book has that rare position of a book that influenced the subject on its own (and all the teaching books that came after).
		The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison, Wisconsin, U.S.A. (Studies in logic and the foundations of mathematics)
	www.hotelresource.com /bookstore/authorsearch_Stephen%20Cole%20Kleene/mode_books.html (298 words)

	Learn more about Stephen Cole Kleene in the online encyclopedia. (Site not responding. Last check: 2007-10-07)
		Learn more about Stephen Cole Kleene in the online encyclopedia.
		Hint: Play with putting spaces before and after your words to see the different results you get.
		He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C
	www.onlineencyclopedia.org /s/st/stephen_cole_kleene.html (496 words)

	STE from FOLDOC
		Stephen P. Jobs (born 24 February 1955).
		Previous: Stephen Cole Kleene, Stephen Jobs, Stephen Kleene, Stepstone Corp, stepwise refinement
		Version 1.7 has been ported to Sequent, Sun, NeXT, Ultrix, BSDI and is available from comp.sources.unix volume 26.
	www.instantweb.com /d/dictionary/foldoc.cgi?query=STE (1117 words)

	Kleene, Stephen Cole (Site not responding. Last check: 2007-10-07)
		Kleene's research was devoted to the theory of algorithms and recursive functions (i.e., functions defined in a finite sequence of combinatorial steps).
		Kleene, together with Alonzo Church, Kurt Gödel, Alan Turing, and others, developed the field of
		Kleene was the author of Introduction to Metamathematics (1952) and Mathematical Logic (1967).
	www.cs.auc.dk /~luca/FS2/kleene-britannica.html (162 words)

	Stephen Cole Kleene, mathematician (Regular Expressions), dies at 85 January 25 in History
		Stephen Cole Kleene, mathematician (Regular Expressions), dies at 85 January 25 in History
		Stephen Cole Kleene, mathematician (Regular Expressions), dies at 85
		During the first period of a man's life the greatest danger is not to take the risk.
	www.brainyhistory.com /events/1994/january_25_1994_169372.html (52 words)

	Define Stephen Kleene : powered by In Dictionary (InDicitonary.com) (Site not responding. Last check: 2007-10-07)
		Define Stephen Kleene : powered by In Dictionary (InDicitonary.com)
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		"stephen kleene" foldoc "The Free On-line Dictionary of Computing (27 SEP 03)"
	www.indictionary.com /define/Stephen_Kleene (546 words)

	Stephen Kleene ; Mathematical Logic, Stephen Kotkin - Armageddon Averted, (Site not responding. Last check: 2007-10-07)
		Stephen Kleene ; Mathematical Logic, Stephen Kotkin - Armageddon Averted,
		Stephen Krensky Marc Tolon Brown - Binky Rules
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	www.virtual-life.com /220733_stephen-kleene.html (169 words)

	Stephen Kleene - OneLook Dictionary Search (Site not responding. Last check: 2007-10-07)
		We found 2 dictionaries with English definitions that include the word Stephen Kleene:
		Tip: Click on the first link on a line below to go directly to a page where "Stephen Kleene" is defined.
		Stephen Kleene : Free On-line Dictionary of Computing [home, info]
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=Stephen+Kleene (81 words)

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