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Kleene's recursion theorem

In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first proved by Stephen Kleene in 1938 and appear in his 1952 book Introduction to Metamathematics. A related theorem, which constructs fixed points of a computable function, is…

The first recursion theorem, Rogers's fixed-point theorem & Kleene's second recursion theorem

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The first recursion theorem

CodeFinite setNatural numberOrdered pairEnumeration reducibility
12 related topics

Rogers's fixed-point theorem

EffectiveS m n theoremY combinatorRecursively enumerableTuring degree
6 related topics

Kleene's second recursion theorem

LispΜ-recursionTuring machinesReflective
4 related topics

Notation

Admissible numberingPartial recursive functionsPartial functions
3 related topics

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Notation

Rogers's fixed-point theorem

Kleene's second recursion theorem

The first recursion theorem

Generalized theorem

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Kleene's recursion theorem

Nodes42
Edges41
Triples9
Avg. degree1.95
Density0.047619
Components1

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Kleene's recursion theorem

Top relations

related to Generalized theorem · 6
Kleene's recursion theorem → Ershov, Given, Gödel, In, Kleene, Kleene's

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theorem recursion function displaystyle computable recursive first fixed second functions operator point varphi enumeration partial index equations set theory fixed-point

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
successorinstance ofreplace instructions0.80text
jumpinstance ofreplace instructions0.80text
remove linesinstance ofreplace instructions0.80text
Kleene's recursion theoremrelated to Generalized theoremIn0.60section
Kleene's recursion theoremrelated to Generalized theoremErshov0.60section
Kleene's recursion theoremrelated to Generalized theoremKleene's0.60section
Kleene's recursion theoremrelated to Generalized theoremGödel0.60section
Kleene's recursion theoremrelated to Generalized theoremKleene0.60section
Kleene's recursion theoremrelated to Generalized theoremGiven0.60section

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