Reducibility of Computable Metrics on the Real Line

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study computable reducibility of computable metrics on 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.

Original languageEnglish
Pages (from-to)302-317
Number of pages16
JournalAlgebra and Logic
Volume56
Issue number4
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Cauchy representation
  • computable metric space
  • reducibility of representations

Fingerprint

Dive into the research topics of 'Reducibility of Computable Metrics on the Real Line'. Together they form a unique fingerprint.

Cite this