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Sibirsk. Mat. Zh., 2017, Volume 58, Number 3, Pages 710–716 (Mi smj2891)  

This article is cited in 1 scientific paper (total in 1 paper)

Minimal generalized computable enumerations and high degrees

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, Kazan, Russia

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.

Keywords: generalized computable enumeration, minimal enumeration, high set, Low$_2$ set, arithmetic enumeration.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1515.2017/ПЧ
Russian Foundation for Basic Research 15-01-08252
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).


DOI: https://doi.org/10.17377/smzh.2017.58.318

Full text: PDF file (287 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:3, 553–558

Bibliographic databases:

UDC: 510.54+510.57
MSC: 35R30
Received: 03.03.2016
Revised: 13.12.2016

Citation: M. Kh. Faizrahmanov, “Minimal generalized computable enumerations and high degrees”, Sibirsk. Mat. Zh., 58:3 (2017), 710–716; Siberian Math. J., 58:3 (2017), 553–558

Citation in format AMSBIB
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\by M.~Kh.~Faizrahmanov
\paper Minimal generalized computable enumerations and high degrees
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 3
\pages 710--716
\mathnet{http://mi.mathnet.ru/smj2891}
\crossref{https://doi.org/10.17377/smzh.2017.58.318}
\elib{http://elibrary.ru/item.asp?id=29160460}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 3
\pages 553--558
\crossref{https://doi.org/10.1134/S0037446617030181}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Siberian Math. J., 58:6 (2017), 1104–1110  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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