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Stephen Cole Kleene (/ ˈ k l eɪ n i / KLAY-nee; [a] January 5, 1909 – January 25, 1994) 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 ...
The predicates can be used to obtain Kleene's normal form theorem for computable functions (Soare 1987, p. 15; Kleene 1943, p. 52—53). This states there exists a fixed primitive recursive function such that a function : is computable if and only if there is a number such that for all , …, one has
Semantical systems claiming to capture such intuitions, due to offering meaningful concepts of “constructive truth” (rather than merely validity or provability), are Kurt Gödel’s dialectica interpretation, Stephen Cole Kleene’s realizability, Yurii Medvedev’s logic of finite problems, [2] or Giorgi Japaridze’s computability logic ...
The paradoxes, Kleene discusses Intuitionism and Formalism in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Stephen Cole Kleene and Richard Eugene Vesley, The Foundations of Intuitionistic Mathematics, North-Holland Publishing Co. Amsterdam ...
An illustration of how the levels of the hierarchy interact and where some basic set categories lie within it. In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define them.
The Church–Turing Thesis: Stephen Kleene, in Introduction To Metamathematics, finally goes on to formally name "Church's Thesis" and "Turing's Thesis", using his theory of recursive realizability. Kleene having switched from presenting his work in the terminology of Church-Kleene lambda definability, to that of Gödel-Kleene recursiveness ...
Numerous results in recursion theory were obtained in the 1940s by Stephen Cole Kleene and Emil Leon Post. Kleene [36] introduced the concepts of relative computability, foreshadowed by Turing, [37] and the arithmetical hierarchy. Kleene later generalized recursion theory to higher-order functionals.
In mathematics and theoretical computer science, a Kleene algebra (/ ˈ k l eɪ n i / KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set supporting union (addition), concatenation (multiplication), and Kleene star operations subject to certain algebraic laws.