Abstract: Under study is the ordering $ {\mathcal{CM}}_{c}({\mathbf{X}}) $ of$ c $-degrees of computable metrics on a Polish space $ {\mathbf{X}} $ with a distinguished dense subset.We prove that this ordering forms a lower semilattice.If, for a computable metric $ \rho $ on $ {\mathbf{X}} $, there isa computable limit point in $ (X,\rho) $; it is possible to construct a computablemetric $ \rho^{\prime}<_{c}\rho $. Under the same assumption, there exists a computablemetric $ \widehat{\rho} $ such that $ \deg_{c}(\rho) $ and $ \deg_{c}(\widehat{\rho}) $have no common upper bounds in $ {\mathcal{CM}}_{c}({\mathbf{X}}) $; thus, in this case$ {\mathcal{CM}}_{c}({\mathbf{X}}) $ is neither an updirected poset nor an upper semilattice.

Cite: Kornev R.A.
A Semilattice of Degrees of Computable Metrics
Siberian Mathematical Journal. 2021. V.62. N5. P.822-841. DOI: 10.1134/S0037446621050050 WOS Scopus OpenAlex

Original: Корнев Р.А.
Полурешетка степеней вычислимых метрик
Сибирский математический журнал. 2021. Т.62. №5. С.1013-1038. DOI: 10.33048/smzh.2021.62.505 OpenAlex

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Web of science:	WOS:000698762500005
Scopus:	2-s2.0-85115613924
OpenAlex:	W3204270394

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Scopus	2
OpenAlex	1
Web of science	2

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