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Algebra Logika, 2017, Volume 56, Number 4, Pages 453–476 (Mi al808)  

This article is cited in 1 scientific paper (total in 1 paper)

Reducibility of computable metrics on the real line

R. A. Kornev

Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: We study computable reducibility of computable metrics on $\mathbf R$ induced by reducibility of their respective Cauchy representations. It is proved that this ordering has a subordering isomorphic to an arbitrary countable tree. Also we introduce a weak version of computable reducibility and construct a countable antichain of computable metrics that are incomparable with respect to it. Informally, copies of the real line equipped with these metrics are pairwise homeomorphic but not computably homeomorphic.

Keywords: computable metric space, Cauchy representation, reducibility of representations.

DOI: https://doi.org/10.17377/alglog.2017.56.405

Full text: PDF file (245 kB)
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English version:
Algebra and Logic, 2017, 56:4, 302–317

Bibliographic databases:

UDC: 510.5
Received: 13.10.2015
Revised: 16.10.2016

Citation: R. A. Kornev, “Reducibility of computable metrics on the real line”, Algebra Logika, 56:4 (2017), 453–476; Algebra and Logic, 56:4 (2017), 302–317

Citation in format AMSBIB
\Bibitem{Kor17}
\by R.~A.~Kornev
\paper Reducibility of computable metrics on the real line
\jour Algebra Logika
\yr 2017
\vol 56
\issue 4
\pages 453--476
\mathnet{http://mi.mathnet.ru/al808}
\crossref{https://doi.org/10.17377/alglog.2017.56.405}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 4
\pages 302--317
\crossref{https://doi.org/10.1007/s10469-017-9451-8}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85033371888}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. A. Kornev, “Computable metrics above the standard real metric”, Sib. elektron. matem. izv., 18:1 (2021), 377–392  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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