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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 1, Pages 112–120
DOI: https://doi.org/10.33048/semi.2021.18.035 (Mi semr1375) 		 
Mathematical logic, algebra and number theory

Weak reducibility of computable and generalized computable numberings

Z. K. Ivanova, M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, 18, Kremlyovskaya str., Kazan, 420008, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.035
Abstract: We consider universal and minimal computable numberings with respect to weak reducibility. A family of total functions that have a universal numbering and two non-weakly equivalent computable numberings is constructed. A sufficient condition for the non-existence of minimal $A$-computable numberings of families with respect to weak reducibility is found for every oracle $A$.
Keywords: computable numbering, $w$-reducibility, $A$-computable numbering, Rogers semilattice.
Funding agency Grant number
Russian Science Foundation 18-11-00028
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1478
The work is supported by the Russian Science Foundation (grant no. 18-11-00028) and performed under the development program of Volga Region Mathematical Center (agreement no.075-02-2020-1478).
Received January 28, 2021, published May 12, 2021
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 03D45
Language: English
Citation: Z. K. Ivanova, M. Kh. Faizrahmanov, “Weak reducibility of computable and generalized computable numberings”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 112–120
Citation in format AMSBIB
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\by Z.~K.~Ivanova, M.~Kh.~Faizrahmanov
\paper Weak reducibility of computable and generalized computable numberings
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 112--120
\mathnet{http://mi.mathnet.ru/semr1375}
\crossref{https://doi.org/10.33048/semi.2021.18.035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000651769300001}
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