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Isolation from Side in 2-Computably Enumerable Degrees

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Abstract

In this work we consider isolation from side in different degree structures, in particular, in the 2-computably enumerable wtt-degrees and in low Turing degrees. Intuitively, a 2-computably enumerable degree is isolated from side if all computably enumerable degrees from its lower cone are bounded from above by some computably enumerable degree which is incomparable with the given one. It is proved that any properly 2-computably enumerable wtt-degree is isolated from side by some computable enumerable wtt-degree. Also it is shown that the same result holds for the low 2-computable enumerable Turing degrees.

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Funding

The work is supported by Russian Foundation for Basic Research (project no. 18-31-00420 mol_a).

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Authors and Affiliations

  1. Kazan Federal University, 18 Kremlyovskaya str., 420008, Kazan, Russia

    M. M. Yamaleev

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  1. M. M. Yamaleev
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Correspondence to M. M. Yamaleev.

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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 8, pp. 81–86.

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Yamaleev, M.M. Isolation from Side in 2-Computably Enumerable Degrees. Russ Math. 64, 70–73 (2020). https://doi.org/10.3103/S1066369X20080095

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  • DOI: https://doi.org/10.3103/S1066369X20080095

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