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Reducibility of Computable Metrics on the Real Line. / Kornev, R. A.

In: Algebra and Logic, Vol. 56, No. 4, 01.09.2017, p. 302-317.

Research output: Contribution to journal › Article › peer-review

Harvard

Kornev, RA 2017, 'Reducibility of Computable Metrics on the Real Line', Algebra and Logic, vol. 56, no. 4, pp. 302-317. https://doi.org/10.1007/s10469-017-9451-8

APA

Kornev, R. A. (2017). Reducibility of Computable Metrics on the Real Line. Algebra and Logic, 56(4), 302-317. https://doi.org/10.1007/s10469-017-9451-8

Vancouver

Kornev RA. Reducibility of Computable Metrics on the Real Line. Algebra and Logic. 2017 Sept 1;56(4):302-317. doi: 10.1007/s10469-017-9451-8

Author

Kornev, R. A. / Reducibility of Computable Metrics on the Real Line. In: Algebra and Logic. 2017 ; Vol. 56, No. 4. pp. 302-317.

BibTeX

@article{98301233ddda4eebb335522c75f84810,
title = "Reducibility of Computable Metrics on the Real Line",
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.",
keywords = "Cauchy representation, computable metric space, reducibility of representations",
author = "Kornev, {R. A.}",
year = "2017",
month = sep,
day = "1",
doi = "10.1007/s10469-017-9451-8",
language = "English",
volume = "56",
pages = "302--317",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "4",

}

RIS

TY - JOUR

T1 - Reducibility of Computable Metrics on the Real Line

AU - Kornev, R. A.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Cauchy representation

KW - computable metric space

KW - reducibility of representations

UR - http://www.scopus.com/inward/record.url?scp=85033371888&partnerID=8YFLogxK

U2 - 10.1007/s10469-017-9451-8

DO - 10.1007/s10469-017-9451-8

M3 - Article

AN - SCOPUS:85033371888

VL - 56

SP - 302

EP - 317

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 4

ER -

ID: 9700026