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Algebra Logika, 2017, Volume 56, Number 4, Pages 506–521 (Mi al811)  

This article is cited in 2 scientific papers (total in 2 papers)

Universal generalized computable numberings and hyperimmunity

M. Kh. Faizrakhmanov

Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008 Russia

Abstract: Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for generalized computable numberings to be precomplete. In addition, we look into the question on boundedness of universal numberings computable relative to high oracles.

Keywords: generalized computable numbering, universal numbering, precomplete numbering, hyperimmune set, high set.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1515.2017/4.6
Russian Foundation for Basic Research 15-01-08252
The work was carried out at the expense of the subsidy allocated to Kazan (Volga Region) Federal University for the fulfillment of the state task in the sphere of scientific activity (project No. 1.1515.2017/4.6) and supported by RFBR (project No. 15-01-08252).


DOI: https://doi.org/10.17377/alglog.2017.56.408

Full text: PDF file (194 kB)
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English version:
Algebra and Logic, 2017, 56:4, 337–347

Bibliographic databases:

Document Type: Article
UDC: 510.54+510.57
Received: 14.07.2015
Revised: 21.03.2017

Citation: M. Kh. Faizrakhmanov, “Universal generalized computable numberings and hyperimmunity”, Algebra Logika, 56:4 (2017), 506–521; Algebra and Logic, 56:4 (2017), 337–347

Citation in format AMSBIB
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\paper Universal generalized computable numberings and hyperimmunity
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\pages 506--521
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\crossref{https://doi.org/10.17377/alglog.2017.56.408}
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\jour Algebra and Logic
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\pages 337--347
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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. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Positive presentations of families relative to $e$-oracles”, Siberian Math. J., 59:4 (2018), 648–656  mathnet  crossref  crossref  isi  elib
    2. S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra and Logic, 57:4 (2018), 275–288  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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