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In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set. These sets arise in the study of computability theory itself, particularly in relation to Π01 classes. Computably inseparable sets also arise in the study of Gödel's incompleteness theorem.

Attributes	Values
rdfs:label	Computably inseparable (en) 帰納的分離不能対 (ja)
rdfs:comment	In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set. These sets arise in the study of computability theory itself, particularly in relation to Π01 classes. Computably inseparable sets also arise in the study of Gödel's incompleteness theorem. (en) 計算可能性理論において帰納的分離不能対（きのうてきぶんりふのうつい、英: recursively inseparable pair)とは自然数の集合の対で帰納的集合によって分離できないものをいう(Monk 1976, p. 100)。この概念は計算理論におけるΠ1集合と関係が深い。帰納的分離不能対はゲーデルの不完全性定理とも関係する。 (ja)
dcterms:subject	Computability theory
Wikipage page ID	26004614 (xsd:integer)
Wikipage revision ID	1030696284 (xsd:integer)
Link from a Wikipage to another Wikipage	Peano arithmetic Computability theory Computably enumerable Computable set William Gasarch Gödel numbering Gödel's incompleteness theorem Computability theory Springer-Verlag Pi01 class Partial computable function
Link from a Wikipage to an external page	https://archive.org/details/mathematicallogi00jdon
sameAs	Computably inseparable Computably inseparable Computably inseparable
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist dbt:Su dbt:Overbar
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has abstract	In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set. These sets arise in the study of computability theory itself, particularly in relation to Π01 classes. Computably inseparable sets also arise in the study of Gödel's incompleteness theorem. (en) 計算可能性理論において帰納的分離不能対（きのうてきぶんりふのうつい、英: recursively inseparable pair)とは自然数の集合の対で帰納的集合によって分離できないものをいう(Monk 1976, p. 100)。この概念は計算理論におけるΠ1集合と関係が深い。帰納的分離不能対はゲーデルの不完全性定理とも関係する。 (ja)
prov:wasDerivedFrom	wikipedia-en:Computably_inseparable?oldid=1030696284&ns=0
page length (characters) of wiki page	3376 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Computably_inseparable
is Link from a Wikipage to another Wikipage of	Recursively inseparable sets Effectively inseparable Effectively inseparable sets Effectively separable Effectively separable set Effectively separable sets Recursive inseparability Recursively inseparable Recursively separable Recursively separable sets
is Wikipage redirect of	Recursively inseparable sets Effectively inseparable Effectively inseparable sets Effectively separable Effectively separable set Effectively separable sets Recursive inseparability Recursively inseparable Recursively separable Recursively separable sets
is foaf:primaryTopic of	wikipedia-en:Computably_inseparable

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