Abstract
If ν and μ are some Δ 02 -computable numberings of families of sets of the naturals then P(x,y) ⇔ ν(x)′ ≠ μ(y) is a Σ 02 -predicate. Deriving corollaries from this result, we obtain a sufficient condition for existence of a Δ 02 -computable numbering of the subfamily of all sets in a given family with the Turing jumps belonging to a fixed level of the Ershov hierarchy, and we deduce existence of a Σ −1ω -computable numbering of the family of all superlow sets.
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Original Russian Text Copyright © 2010 Faizrahmanov M. Kh.
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Faizrahmanov, M. Computable numberings of families of low sets and Turing jumps in the Ershov hierarchy. Sib Math J 51, 1135–1138 (2010). https://doi.org/10.1007/s11202-010-0111-7
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DOI: https://doi.org/10.1007/s11202-010-0111-7