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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 1, Pages 31–41
DOI: https://doi.org/10.33048/smzh.2021.62.103 (Mi smj7535) 		 
On universal pairs in the Ershov hierarchy

N. A. Bazhenovab, M. Mustafac, S. S. Ospichevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Nazarbayev University, Nur-Sultan, Kazakhstan
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DOI: https://doi.org/10.33048/smzh.2021.62.103
Abstract: We develop the Ershov theory of $C$-classes for some finite families of sets in the Ershov hierarchy. We generalize the result by Muchnik on multiple $m$-reducibility as follows: There exists an $m$-universal pair of disjoint sets for each level of the Ershov hierarchy.
Keywords: Ershov hierarchy, $m$-reducibility, $C$-class, computable numbering.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075–15–2019–1613
Nazarbayev University Faculty Development Competitive Research Grants 090118FD5342
Ministry of Education and Science of the Republic of Kazakhstan AP08856834
N. A. Bazhenov and S. S. Ospichev were supported by the Mathematical Center in Akademgorodok (Agreement 075–15–2019–1613 with the Ministry of Science and Higher Education). M. Mustafa was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342 and partially supported by the MES RK Grant AP08856834.
Received: 07.05.2020
Revised: 18.09.2020
Accepted: 09.10.2020
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 1, Pages 23–31
DOI: https://doi.org/10.1134/S0037446621010031
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 35R30
Language: Russian
Citation: N. A. Bazhenov, M. Mustafa, S. S. Ospichev, “On universal pairs in the Ershov hierarchy”, Sibirsk. Mat. Zh., 62:1 (2021), 31–41; Siberian Math. J., 62:1 (2021), 23–31
Citation in format AMSBIB
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