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Algebra i logika, 2017, Volume 56, Number 4, Pages 453–476
DOI: https://doi.org/10.17377/alglog.2017.56.405 (Mi al808) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Reducibility of computable metrics on the real line

R. A. Kornev

Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
Full-text PDF (245 kB) Citations (4)
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DOI: https://doi.org/10.17377/alglog.2017.56.405
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.
Received: 13.10.2015
Revised: 16.10.2016
English version:
Algebra and Logic, 2017, Volume 56, Issue 4, Pages 302–317
DOI: https://doi.org/10.1007/s10469-017-9451-8
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
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
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
     
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