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Matematicheskie Trudy, 2023, Volume 26, Number 1, Pages 47–92
DOI: https://doi.org/10.33048/mattrudy.2023.26.104 (Mi mt689) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Negative numberings in admissible sets. I

I. Sh. Kalimullinab, V. G. Puzarenkocd, M. Kh. Faizrahmanovab

a Kazan Federal University, Kazan, 420008, Russia
b Scientific-Educational Mathematical Center of Volga Federal District
c Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
d Novosibirsk State University, Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/mattrudy.2023.26.104
Abstract: We construct an admissible set $\mathbb{A}$ such that the family of all $\mathbb{A}$-computably enumerable sets possesses a negative computable $\mathbb{A}$-numbering but lacks positive computable $\mathbb{A}$-numberings. We also discuss the question on existence of minimal negative $\mathbb{A}$-numberings.
Key words: numbering, decidable numbering, positive numbering, negative numbering, computable numbering, computable set, computably enumerable set, admissible set.
Funding agency Grant number
Russian Science Foundation 18-11-00028
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1393
Received: 25.05.2023
Revised: 14.06.2023
Accepted: 16.06.2023
English version:
Siberian Advances in Mathematics, 2023, Volume 33, Issue 4, Pages 293–321
DOI: https://doi.org/10.1134/S105513442304003X
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Negative numberings in admissible sets. I”, Mat. Tr., 26:1 (2023), 47–92; Siberian Adv. Math., 33:4 (2023), 293–321
Citation in format AMSBIB
\Bibitem{KalPuzFai23}
\by I.~Sh.~Kalimullin, V.~G.~Puzarenko, M.~Kh.~Faizrahmanov
\paper Negative numberings in admissible sets.~I
\jour Mat. Tr.
\yr 2023
\vol 26
\issue 1
\pages 47--92
\mathnet{http://mi.mathnet.ru/mt689}
\crossref{https://doi.org/10.33048/mattrudy.2023.26.104}
\elib{https://elibrary.ru/item.asp?id=54901440}
\transl
\jour Siberian Adv. Math.
\yr 2023
\vol 33
\issue 4
\pages 293--321
\crossref{https://doi.org/10.1134/S105513442304003X}
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