# Stephen Cole Kleene

American mathematician and theoretical computer scientist

## Stephen Cole Kleene's AcademicInfluence.com Rankings

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Computer Science Mathematics

## Stephen Cole Kleene's Degrees

- PhD Mathematics Princeton University
- Bachelors Mathematics Amherst College

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## Why Is Stephen Cole Kleene Influential?

(Suggest an Edit or Addition)According to Wikipedia, Stephen Cole Kleene was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star , Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism.

## Stephen Cole Kleene's Published Works

### Published Works

- Introduction to Metamathematics (1952) (4165)
- Representation of Events in Nerve Nets and Finite Automata (1951) (1779)
- On notation for ordinal numbers (1938) (675)
- On the interpretation of intuitionistic number theory (1945) (536)
- General recursive functions of natural numbers (1936) (502)
- On undecidable propositions of formal mathematical systems (1934) (333)
- Recursive predicates and quantifiers (1943) (306)
- Recursive functionals and quantifiers of finite types. II (1959) (286)
- The Upper Semi-Lattice of Degrees of Recursive Unsolvability (1954) (256)
- Mathematical Logic (1967) (253)
- $\lambda$-definability and recursiveness (1936) (209)
- The foundations of intuitionistic mathematics : especially in relation to recursive functions (1965) (187)
- λ-Definability and Recursiveness. (1937) (137)
- Arithmetical predicates and function quantifiers (1955) (136)
- Origins of recursive function theory (1979) (126)
- Hierarchies of number-theoretic predicates (1955) (123)
- On the Forms of the Predicates in the Theory of Constructive Ordinals (Second Paper) (1955) (115)
- A Theory of Positive Integers in Formal Logic. Part II (1935) (104)
- The Foundations of Intuitionistic Mathematics. (1967) (100)
- On the Forms of the Predicates in the Theory of Constructive Ordinals (1944) (92)
- Disjunction and existence under implication in elementary intuitionistic formalisms (1962) (91)
- Formalized Recursive Functionals and Formalized Realizability (1969) (83)
- Formal definitions in the theory of ordinal numbers (1937) (82)
- Recursive functionals and quantifiers of finite types revisited. V (1991) (77)
- Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols (1952) (73)
- Collected Works, Volume I, Publications 1929-1936 (1987) (71)
- Extension of an effectively generated class of functions by enumeration (1958) (64)
- Origins of Recursive Function Theory (1979) (60)
- Quantification of number-theoretic functions (1960) (57)
- The Inconsistency of Certain Formal Logics (1935) (54)
- Realizability: A retrospective survey (1973) (52)
- Reflections on Church's thesis (1987) (49)
- Turing's analysis of computability, and major applications of it (1988) (46)
- General Recursive Functions of Natural Numbers. (1937) (39)
- Review: Emil L. Post, Recursive Unsolvability of a Problem of Thue (1947) (36)
- Turing-Machine Computable Functionals of Finite Types I (1966) (31)
- Kurt Godel: collected works. Vol. 1: Publications 1929-1936 (1986) (31)
- Turing-machine computable func-tionals of nite types II (1962) (30)
- Two papers on the predicate calculus (1952) (27)
- The work of Kurt Gödel (1976) (24)
- A note on recursive functions (1936) (21)
- Proof by Cases in Formal Logic (1934) (20)
- A note on function quantification (1957) (17)
- Lambda-definable functionals of finite types (1962) (15)
- Kurt Gödel: Collected Works Vol. Ii (1990) (10)
- Algorithms in various contexts (1979) (8)
- An addendum to “The work of Kurt Gödel” (1978) (8)
- Review: Kurt Godel, What is Cantor's Continuum Problem? (1948) (7)
- Turing A. M.. Solvable and unsolvable problems. Science news (Penguin books, Melbourne–London–Baltimore), no. 31 (1954), pp. 7–23. (1955) (7)
- A Note on Computable Functionals (1956) (6)
- Review: Haskell B. Curry, A Simplification of the Theory of Combinators (1952) (6)
- Review: Rudolf Carnap, The Logical Syntax of Language (1939) (6)
- On Undecidable Propositions of Formal Mathematical Systems .PostscriptumIntroductory Note to 1934 (1990) (5)
- Constructive Functions in “The Foundations of Intuttionistic Mathematics” (1968) (5)
- Analysis of Lengthening of Modulated Repetitive Pulses (1947) (5)
- Review: E. W. Beth, Semantical Considerations on Intuitionistic Mathematics (1948) (4)
- A Postulational Basis for Probability (1939) (3)
- Review: K. R. Popper, On the Theory of Deduction, Part I. Derivation and its Generalizations; K. R. Popper, On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation; K. R. Popper, The Trivialization of Mathematical Logic (1949) (3)
- Review: K. R. Popper, Functional Logic Without Axioms or Primitive Rules of Inference (1948) (3)
- Review: Frederic B. Fitch, An Extension of Basic Logic (1949) (3)
- Perelman versus Godel. (1937) (2)
- Church Alonzo. Introduction to mathematical logic. Volume I. Second printing. Princeton University Press, Princeton 1958, x + 378 pp. (1958) (2)
- Review: Olaf Helmer, Perelman versus Godel (1937) (1)
- Church Alonzo. The calculi of lambda-conversion. Annals of Mathematics studies, no. 6. Second printing. Lithoprinted. Princeton University Press, Princeton 1951, 82 pp. (1952) (1)
- Review: E. W. Beth, Semantic Construction of Intuitionistic Logic (1957) (1)
- Review: Emil L. Post, Note on a Conjecture of Skolem (1947) (1)
- Third Meeting of the Association for Symbolic Logic (1938) (1)
- Logic and Foundations of Mathematics (1968) (1)
- Review: Haskell B. Curry, Some Aspects of the problem of Mathematical Rigor (1941) (1)
- Beth E. W.. Semantical considerations on intuitionistic mathematics. Koninklijke Nederlandsche Akademie van Wetenschappen, Proceedings of the section of sciences, vol. 50 (1947), pp. 1246–1251, and ibid., pp. 572–577. (1948) (1)
- Reviews. Kurt Gödel. What is Cantor's continuum problem? The American mathematical monthly, vol. 54 (1947), pp. 515–525. (1948) (1)
- An addendum (1963) (1)
- Chapter I A Formal System of Intuitionistic Analysis (1965) (1)
- Sets, logic, and mathematical foundations (1963) (1)
- Review: Edward V. Huntington, Mathematical Postulates for the Logical Operations of Assertion, Conjunction, Negation and Equality (1936) (0)
- Chapter II Various Notions of Realizability (1965) (0)
- Review: Alonzo Church, Introduction to Mathematical Logic (1958) (0)
- Review: Frederic B. Fitch, The Heine-Borel Theorem in Extended Basic Logic (1950) (0)
- The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison, Wisconsin, U.S.A. (1981) (0)
- Post Emil L.. Note on a conjecture of Skolem. The journal of symbolic logic , vol. 11 (1946), pp. 73–74. (1947) (0)
- Review: Alonzo Church, The Calculi of Lambda-Conversion (1952) (0)
- Helmer Olaf. Perelman versus Gödel. Mind, vol. 46 (1937), pp. 58–60. (1937) (0)
- Fitch Frederic B.. The Heine-Borel theorem in extended basic logic. The journal of symbolic logic, vol. 14 (1949), pp. 9–15. (1950) (0)
- Wernick William. Functional dependence in the calculus of propositions. The American mathematical monthly, vol. 47 (1940), pp. 602–605. (1941) (0)
- A Theorem on Parametric Boolean Functions (1958) (0)
- A. J. Kempner. Remarks on “unsolvable” problems. The American mathematical monthly , vol. 43 (1936), pp. 467–473. (1937) (0)
- INTERNATIONAL U NION OF THE H ISTORY AND PHILOSOPHY O F S CIENCE DIVISION O F L OGIC, M ETHODOLOGY A ND P HILOSOPHY OF SCIENCE (1983) (0)
- Review: Rozsa Peter, Contribution to Recursive Number Theory (1940) (0)
- Huntington Edward V.. Mathematical postulates for the logical operations of assertion, conjunction, negation and equality. Proceedings of the National Academy of Sciences, vol. 22 (1936), pp. 291–296. (1936) (0)
- Review: A. G. D. Watson, Mathematics and Its Foundations (1939) (0)
- List of officers and members of the Association for Symbolic Logic (1963) (0)
- Curry H. B.. First properties of functionality in combinatory logic. The Tôhoku mathematical journal, vol. 41 (1936), pp. 371–401. (1936) (0)
- Chapter IV On Order in the Continuum (1965) (0)
- Review: Frederic B. Fitch, A Further Consistent Extension of Basic Logic (1950) (0)
- Review: Arthur H. Copeland, Postulates for the Theory of Probability (1942) (0)
- Popper K. R.. Functional logic without axioms or primitive rules of inference. Koninklijke Nederlandsche Akademie van Wetenschappen, Proceedings of the section of sciences, vol. 50 (1947), pp. 1214–1224, and ibid., pp. 561–571. (1948) (0)
- Review: A. J. Kempner, Remarks on "Unsolvable" Problems (1937) (0)
- Curry Haskell B.. Some aspects of the problem of mathematical rigor. Bulletin of the American Mathematical Society , vol. 47 (1941), pp. 221–241. (1941) (0)
- Remarks on "Unsolvable" Problems. (1937) (0)
- Review: H. B. Curry, First Properties of Functionality in Combinatory Logic (1936) (0)
- Curry Haskell B.. A simplification of the theory of combinators. Synthese, vol. 7 (1948–1949), pp. 391–399. (1952) (0)
- Review: William Wernick, Functional Dependence in the Calculus of Propositions (1941) (0)
- Fitch Frederic B.. A further consistent extension of basic logic, The journal of symbolic logic. vol. 14 (1949), pp. 209–218. (1950) (0)

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