Siberian Mathematical Journal

, Volume 51, Issue 6, pp 1135–1138 | Cite as

Computable numberings of families of low sets and Turing jumps in the Ershov hierarchy

  • M.Kh. FaizrahmanovEmail author


If ν and μ are some Δ 2 0 -computable numberings of families of sets of the naturals then P(x,y) ⇔ ν(x)′ ≠ μ(y) is a Σ 2 0 -predicate. Deriving corollaries from this result, we obtain a sufficient condition for existence of a Δ 2 0 -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 ω −1 -computable numbering of the family of all superlow sets.


computable numbering Ershov hierarchy constructive ordinal low set superlow set 


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

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