Search results
Results from the WOW.Com Content Network
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 ...
Stephen Cole Kleene, 1952. Introduction to Metamathematics. North Holland. Aimed at mathematicians. Jules Richard, Les Principes des Mathématiques et le Problème des Ensembles, Revue Générale des Sciences Pures et Appliquées (1905); translated in Heijenoort J. van (ed.), Source Book in Mathematical Logic 1879-1931 (Cambridge, Massachusetts ...
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.
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.
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 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 ...
Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis" (Kleene 1952:317) (i.e., the Church thesis). Kleene, Stephen Cole (1952). Introduction to Metamathematics. North-Holland.
Stephen Cole Kleene described the result as "not a paradox in the sense of outright contradiction, but rather a kind of anomaly". [33] After surveying Skolem's argument that the result is not contradictory, Kleene concluded: "there is no absolute notion of countability". [33] Geoffrey Hunter described the contradiction as "hardly even a paradox ...