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Algebra Logika, 2018, Volume 57, Number 4, Pages 426–447 (Mi al857)  

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

Some absolute properties of $A$-computable numberings

S. A. Badaeva, A. A. Issakhovab

a Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Alma-Ata, 050038 Kazakhstan
b Kazkh-British Technical University, ul. Tole bi 59, Alma-Ata, 050000 Kazakhstan

Abstract: For an arbitrary set $A$ of natural numbers, we prove the following statements: every finite family of $A$-computable sets containing a least element under inclusion has an $A$-computable universal numbering; every infinite $A$-computable family of total functions has (up to $A$-equivalence) either one $A$-computable Friedberg numbering or infinitely many such numberings; every $A$-computable family of total functions which contains a limit function has no $A$-computable universal numberings, even with respect to $A$-reducibility.

Keywords: $A$-computable numbering, $A$-computable Friedberg numbering, $A$-computable universal numbering, $A$-reducibility.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan AP05132349
Supported by the Science Committee of the Republic of Kazakhstan, grant No. AP05132349.


DOI: https://doi.org/10.17377/alglog.2018.57.402

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English version:
Algebra and Logic, 2018, 57:4, 275–288

Bibliographic databases:

UDC: 510.54
Received: 11.02.2017
Revised: 29.01.2018

Citation: S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra Logika, 57:4 (2018), 426–447; Algebra and Logic, 57:4 (2018), 275–288

Citation in format AMSBIB
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\paper Some absolute properties of $A$-computable numberings
\jour Algebra Logika
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\vol 57
\issue 4
\pages 426--447
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\crossref{https://doi.org/10.17377/alglog.2018.57.402}
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\jour Algebra and Logic
\yr 2018
\vol 57
\issue 4
\pages 275--288
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Kh. Faizrakhmanov, “Reshetochnye svoistva polureshetok Rodzhersa vychislimykh i obobschenno vychislimykh semeistv”, Sib. elektron. matem. izv., 16 (2019), 1927–1936  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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