#428

Most Influential Person

American mathematician and theoretical computer scientist

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.

- Introduction to Metamathematics (1952) (4120)
- Representation of Events in Nerve Nets and Finite Automata (1951) (1756)
- On notation for ordinal numbers (1938) (664)
- On the interpretation of intuitionistic number theory (1945) (529)
- General recursive functions of natural numbers (1936) (499)
- On undecidable propositions of formal mathematical systems (1934) (327)
- Recursive predicates and quantifiers (1943) (304)
- Recursive functionals and quantifiers of finite types. II (1959) (285)
- The Upper Semi-Lattice of Degrees of Recursive Unsolvability (1954) (257)
- Mathematical Logic (1967) (253)
- $\lambda$-definability and recursiveness (1936) (209)
- The foundations of intuitionistic mathematics : especially in relation to recursive functions (1965) (186)
- λ-Definability and Recursiveness. (1937) (137)
- Arithmetical predicates and function quantifiers (1955) (136)
- Origins of recursive function theory (1979) (125)
- Hierarchies of number-theoretic predicates (1955) (122)
- 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) (103)
- The Foundations of Intuitionistic Mathematics. (1967) (99)
- On the Forms of the Predicates in the Theory of Constructive Ordinals (1944) (92)
- Disjunction and existence under implication in elementary intuitionistic formalisms (1962) (89)
- Formal definitions in the theory of ordinal numbers (1937) (82)
- Formalized Recursive Functionals and Formalized Realizability (1969) (82)
- Recursive functionals and quantifiers of finite types revisited. V (1991) (75)
- Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols (1952) (72)
- Collected Works, Volume I, Publications 1929-1936 (1987) (70)
- Extension of an effectively generated class of functions by enumeration (1958) (63)
- Origins of Recursive Function Theory (1979) (58)
- Quantification of number-theoretic functions (1960) (57)
- The Inconsistency of Certain Formal Logics (1935) (54)
- Realizability: A retrospective survey (1973) (51)
- 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)
- Kurt Godel: collected works. Vol. 1: Publications 1929-1936 (1986) (31)
- Turing-Machine Computable Functionals of Finite Types I (1966) (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)
- An addendum to “The work of Kurt Gödel” (1978) (8)
- Algorithms in various contexts (1979) (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: Rudolf Carnap, The Logical Syntax of Language (1939) (6)
- Review: Haskell B. Curry, A Simplification of the Theory of Combinators (1952) (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)
- 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)
- Third Meeting of the Association for Symbolic Logic (1938) (1)
- Sets, logic, and mathematical foundations (1963) (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)
- Logic and Foundations of Mathematics (1968) (1)
- Review: Olaf Helmer, Perelman versus Godel (1937) (1)
- Chapter I A Formal System of Intuitionistic Analysis (1965) (1)
- Review: E. W. Beth, Semantic Construction of Intuitionistic Logic (1957) (1)
- Review: Emil L. Post, Note on a Conjecture of Skolem (1947) (1)
- Review: Haskell B. Curry, Some Aspects of the problem of Mathematical Rigor (1941) (1)
- Reviews. Kurt Gödel. What is Cantor's continuum problem? The American mathematical monthly, vol. 54 (1947), pp. 515–525. (1948) (1)
- 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)
- Review: Frederic B. Fitch, The Heine-Borel Theorem in Extended Basic Logic (1950) (0)
- Review: H. B. Curry, First Properties of Functionality in Combinatory Logic (1936) (0)
- Curry H. B.. First properties of functionality in combinatory logic. The Tôhoku mathematical journal, vol. 41 (1936), pp. 371–401. (1936) (0)
- Curry Haskell B.. A simplification of the theory of combinators. Synthese, vol. 7 (1948–1949), pp. 391–399. (1952) (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)
- An addendum (1963) (0)
- Review: A. G. D. Watson, Mathematics and Its Foundations (1939) (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)
- Chapter II Various Notions of Realizability (1965) (0)
- A. J. Kempner. Remarks on “unsolvable” problems. The American mathematical monthly , vol. 43 (1936), pp. 467–473. (1937) (0)
- Wernick William. Functional dependence in the calculus of propositions. The American mathematical monthly, vol. 47 (1940), pp. 602–605. (1941) (0)
- Review: Rozsa Peter, Contribution to Recursive Number Theory (1940) (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: Alonzo Church, Introduction to Mathematical Logic (1958) (0)
- Helmer Olaf. Perelman versus Gödel. Mind, vol. 46 (1937), pp. 58–60. (1937) (0)
- Remarks on "Unsolvable" Problems. (1937) (0)
- Review: Edward V. Huntington, Mathematical Postulates for the Logical Operations of Assertion, Conjunction, Negation and Equality (1936) (0)
- List of officers and members of the Association for Symbolic Logic (1963) (0)
- Chapter IV On Order in the Continuum (1965) (0)
- Review: A. J. Kempner, Remarks on "Unsolvable" Problems (1937) (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)
- Fitch Frederic B.. The Heine-Borel theorem in extended basic logic. The journal of symbolic logic, vol. 14 (1949), pp. 9–15. (1950) (0)
- Fitch Frederic B.. A further consistent extension of basic logic, The journal of symbolic logic. vol. 14 (1949), pp. 209–218. (1950) (0)
- A Theorem on Parametric Boolean Functions (1958) (0)
- Review: William Wernick, Functional Dependence in the Calculus of Propositions (1941) (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)
- The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison, Wisconsin, U.S.A. (1981) (0)

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