About: Computably inseparable

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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.

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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. (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)
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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. (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)
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  • Computably inseparable (en)
  • 帰納的分離不能対 (ja)
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