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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 ...
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers.Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame."
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 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
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.
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 ...
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.
Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system.