Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2023, Number 3, Pages 28–35
DOI: https://doi.org/10.55959/MSU0579-9368-1-64-3-5 (Mi vmumm4537) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Two theorems on minimal generally-computable numberings

M. Kh. Faizrahmanov

Scientific-Educational Mathematical Center of Volga Federal District
Full-text PDF (248 kB) Citations (2)
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DOI: https://doi.org/10.55959/MSU0579-9368-1-64-3-5
Abstract: The paper proves that for any set $A$ that computes a non-computable computably enumerable set, any infinite $A$-computable family has an infinite number of pairwise nonequivalent minimal $A$-computable numberings. It is established that an arbitrary set $A\leqslant_T\emptyset '$ is low if and only if any infinite $A$-computable family with the greatest set under inclusion has an infinite number of pairwise nonequivalent positive $A$-computable numberings.
Key words: minimal numbering, positive numbering, computably enumerable set, low set.
Funding agency Grant number
Russian Science Foundation 22–21–20024
Program of developing the Scientific and Educational Mathematical Center of the Volga Federal District 075–02–2023–944
Received: 14.11.2022
English version:
Moscow University Mathematics Bulletin, 2023, Volume 78, Issue 3, Pages 136–143
DOI: https://doi.org/10.3103/S0027132223030026
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: M. Kh. Faizrahmanov, “Two theorems on minimal generally-computable numberings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 3, 28–35; Moscow University Mathematics Bulletin, 78:3 (2023), 136–143
Citation in format AMSBIB
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\by M.~Kh.~Faizrahmanov
\paper Two theorems on minimal generally-computable numberings
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2023
\issue 3
\pages 28--35
\mathnet{http://mi.mathnet.ru/vmumm4537}
\crossref{https://doi.org/10.55959/MSU0579-9368-1-64-3-5}
\zmath{https://zbmath.org/?q=an:7741294}
\elib{https://elibrary.ru/item.asp?id=53868403}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2023
\vol 78
\issue 3
\pages 136--143
\crossref{https://doi.org/10.3103/S0027132223030026}
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