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Minimal generalized computable enumerations and high degrees

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Abstract

We establish that the set of minimal generalized computable enumerations of every infinite family computable with respect to a high oracle is effectively infinite. We find some sufficient condition for enumerations of the infinite families computable with respect to high oracles under which there exist minimal generalized computable enumerations that are irreducible to the enumerations.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kazan, Russia

    M. Kh. Faizrahmanov

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  1. M. Kh. Faizrahmanov
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Correspondence to M. Kh. Faizrahmanov.

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Original Russian Text Copyright © 2017 Faizrahmanov M.Kh.

The author was supported by the subsidy of the government task for Kazan (Volga Region) Federal University (Grant 1.1515.2017/PP) and the Russian Foundation for Basic Research (Grant 15–01–08252).

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Faizrahmanov, M.K. Minimal generalized computable enumerations and high degrees. Sib Math J 58, 553–558 (2017). https://doi.org/10.1134/S0037446617030181

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  • DOI: https://doi.org/10.1134/S0037446617030181

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