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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 1, Pages 248–258
DOI: https://doi.org/10.33048/semi.2022.19.019 (Mi semr1496) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical logic, algebra and number theory

On the maximality of degrees of metrics under computable reducibility

R. Kornev

Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.019
Abstract: We study the semilattice $\mathcal{CM}_c(\mathbf{X})$ of degrees of computable metrics on a Polish space $\mathbf{X}$ under computable reducibility. It is proved that this semilattice does not have maximal elements if $\mathbf{X}$ is a noncompact space. It is also shown that the degree of the standard metric on the unit interval is maximal in the respective semilattice.
Keywords: computable metric space, Cauchy representation, reducibility of representations, computable analysis.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-50001
The reported study was funded by RFBR and JSPS, project number 20-51-50001.
Received April 7, 2021, published April 19, 2022
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 03F60
Language: English
Citation: R. Kornev, “On the maximality of degrees of metrics under computable reducibility”, Sib. Èlektron. Mat. Izv., 19:1 (2022), 248–258
Citation in format AMSBIB
\Bibitem{Kor22}
\by R.~Kornev
\paper On the maximality of degrees of metrics under computable reducibility
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 1
\pages 248--258
\mathnet{http://mi.mathnet.ru/semr1496}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4410451}
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