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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 ...
Kleene's work with the proof theory of intuitionistic logic showed that constructive information can be recovered from intuitionistic proofs. For example, any provably total function in intuitionistic arithmetic is computable ; this is not true in classical theories of arithmetic such as Peano arithmetic .
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.
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.
Stephen Cole Kleene, 1934 Simon B. Kochen, 1959 Maurice L'Abbé, 1951 Isaac Malitz, 1976 Gary R. Mar, 1985 Michael O. Rabin, 1957 Nicholas Rescher, 1951 Hartley Rogers, Jr, 1952 J. Barkley Rosser, 1934 Dana Scott, 1958 Norman Shapiro, 1955 Raymond Smullyan, 1959 Alan Turing, 1938 [1]
Computability theory originated in the 1930s, with the work of Kurt Gödel, Alonzo Church, Rózsa Péter, Alan Turing, Stephen Kleene, and Emil Post. [3] [b]The fundamental results the researchers obtained established Turing computability as the correct formalization of the informal idea of effective calculation.
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 ...
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.