Geodesic
On the maximality of degrees of metrics under computable reducibility
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 248-258.

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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. 
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R. Kornev. On the maximality of degrees of metrics under computable reducibility. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 248-258. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/

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