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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 ...
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.
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
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.
Regular expressions originated in 1951, when mathematician Stephen Cole Kleene described regular languages using his mathematical notation called regular events. [ 6 ] [ 7 ] These arose in theoretical computer science , in the subfields of automata theory (models of computation) and the description and classification of formal languages ...
Intuitionistic logic has found practical use in mathematics despite the challenges presented by the inability to utilize these rules. One reason for this is that its restrictions produce proofs that have the disjunction and existence properties, making it also suitable for other forms of mathematical constructivism.
Kleene (1938) described a system of notation for all recursive ordinals (those less than the Church–Kleene ordinal). Unfortunately, unlike the other systems described above there is in general no effective way to tell whether some natural number represents an ordinal, or whether two numbers represent the same ordinal.
[1] The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the ...