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Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability…

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Overview

Introduction

Turing computability

Areas of research

Relationships between definability, proof and computability

Name

Professional organizations

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Computability theory

Nodes132
Edges131
Triples160
Avg. degree1.98
Density0.015152
Components1

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Computability theory

Top relations

related to Further reading · 38
Computability theory → André, Arun, Barry, Bradford Book, Chapman, Classical Recursion Theory, Computability, Cooper, Daniel Nathan, Degrees, Elsevier, Hall/CRC, Hilbert's Tenth Problem, II, ISBN, Jain, James, LCCN, Lerman, Manuel
related to Name · 18
Computability theory → According, Erlangen, Euclidean, Fortnow, He, In, Kleene, Many, Not, Robert, Rogers, Simpson, Since, Soare, Some, The, These, Turing's
related to Frequency computation · 17
Computability theory → After, Beigel's, Degtev, For, Jockusch, Jockusch's, Kummer's, Later, On, One, Russian, Such, The, There, This, Trakhtenbrot's, Turing
related to Introduction · 17
Computability theory → Alan Turing, Alonzo Church, Although, Church, Church's, Computability, Emil Post, Gödel, In, Kleene, Kurt Gödel, Nowadays, Rózsa Péter, Stephen Kleene, The, Turing, Turing's
related to Relationships between definability, proof and computability · 12
Computability theory → Computability, Gödel's, In, Kurt Gödel, One, Post's, Similarly, Simpson, Tarski's, The, There, Turing
related to The priority method · 11
Computability theory → Because, Each, For, Friedberg, It, Kummer, Post's, Priority, The, This, To
related to Relative computability and the Turing degrees · 10
Computability theory → An, Computability, Each, If, Informally, Is, The, The Turing, Thus, Turing
related to Generalizations of Turing computability · 7
Computability theory → Both Turing, Computability, Pi, Sacks, The, These, Turing
related to Professional organizations · 6
Computability theory → Association, Association Computability, CiE, Europe, Symbolic Logic, The
related to Continuous computability theory · 5
Computability theory → Blum, Computability, For, Shub, Smale

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Important terminology

computable sets turing computability set theory enumerable computably problem natural numbers also function reducibility functions study degrees recursive many halting

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Computability theoryis aAssociation for Symbolic Logic0.90text
arithmetic reducibilityinstance ofMany related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 196…0.80text
hyperarithmetical reducibilityinstance ofMany related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 196…0.80text
α-recursion theoryinstance ofMany related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 196…0.80text
as described by Sacks in 1990instance ofMany related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 196…0.80text
the Bluminstance ofmodels of computation0.80text
arithmetic reducibilityinstance ofGeneralizations of Turing computabilityComputability theory includes the study of generalized notions of this field0.80text
hyperarithmetical reducibilityinstance ofGeneralizations of Turing computabilityComputability theory includes the study of generalized notions of this field0.80text
α-recursion theoryinstance ofGeneralizations of Turing computabilityComputability theory includes the study of generalized notions of this field0.80text
as described by Sacks in 1990instance ofGeneralizations of Turing computabilityComputability theory includes the study of generalized notions of this field0.80text
partial computable functioninstance ofThese researchers also use terminology0.80text
computably enumerableinstance ofThese researchers also use terminology0.80text

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