Standard

Computable metrics above the standard real metric. / Kornev, R.

In: Siberian Electronic Mathematical Reports, Vol. 18, No. 1, 29, 2021, p. 377-392.

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

Harvard

Kornev, R 2021, 'Computable metrics above the standard real metric', Siberian Electronic Mathematical Reports, vol. 18, no. 1, 29, pp. 377-392. https://doi.org/10.33048/semi.2021.18.027

APA

Kornev, R. (2021). Computable metrics above the standard real metric. Siberian Electronic Mathematical Reports, 18(1), 377-392. [29]. https://doi.org/10.33048/semi.2021.18.027

Vancouver

Kornev R. Computable metrics above the standard real metric. Siberian Electronic Mathematical Reports. 2021;18(1):377-392. 29. doi: 10.33048/semi.2021.18.027

Author

Kornev, R. / Computable metrics above the standard real metric. In: Siberian Electronic Mathematical Reports. 2021 ; Vol. 18, No. 1. pp. 377-392.

BibTeX

@article{666492a6ba9a4713b7be2af438a480b3,
title = "Computable metrics above the standard real metric",
abstract = "We construct a sequence of computable real metrics pairwise incomparable under weak reducibility < ch and located above the standard real metric w. r. t. computable reducibility <c. Iterating the construction, we obtain that the ordering (P(ω), ⸦) of subsets of ω is embeddable into the ordering of ch-degrees of real metrics above the standard metric. It is also proved that the countable atomless Boolean algebra is embeddable with preservation of joins and meets into the ordering of c-degrees of computable real metrics.",
keywords = "Cauchy representation, computable analysis, computable metric space, reducibility of representations, representation of real numbers",
author = "R. Kornev",
note = "Funding Information: Kornev, R., Computable metrics above the standard real metric. {\textcopyright} 2021 Kornev R. The research was supported by RFBR, project 19-31-50006 mol_nr, and was partially carried out while the author was visiting Lobachevsky Institute of Mathematics and Mechanics of Kazan Federal University. The author wants to thank Kazan Federal University for hospitality and I. Sh. Kalimullin and M. M. Yamaleev for useful discussions. The author is grateful to the referee for numerous valuable and constructive comments. Received August, 6, 2019, published April, 13, 2021. Publisher Copyright: {\textcopyright} 2021 Kornev R. All Rights Reserved.",
year = "2021",
doi = "10.33048/semi.2021.18.027",
language = "English",
volume = "18",
pages = "377--392",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Computable metrics above the standard real metric

AU - Kornev, R.

N1 - Funding Information: Kornev, R., Computable metrics above the standard real metric. © 2021 Kornev R. The research was supported by RFBR, project 19-31-50006 mol_nr, and was partially carried out while the author was visiting Lobachevsky Institute of Mathematics and Mechanics of Kazan Federal University. The author wants to thank Kazan Federal University for hospitality and I. Sh. Kalimullin and M. M. Yamaleev for useful discussions. The author is grateful to the referee for numerous valuable and constructive comments. Received August, 6, 2019, published April, 13, 2021. Publisher Copyright: © 2021 Kornev R. All Rights Reserved.

PY - 2021

Y1 - 2021

N2 - We construct a sequence of computable real metrics pairwise incomparable under weak reducibility < ch and located above the standard real metric w. r. t. computable reducibility <c. Iterating the construction, we obtain that the ordering (P(ω), ⸦) of subsets of ω is embeddable into the ordering of ch-degrees of real metrics above the standard metric. It is also proved that the countable atomless Boolean algebra is embeddable with preservation of joins and meets into the ordering of c-degrees of computable real metrics.

AB - We construct a sequence of computable real metrics pairwise incomparable under weak reducibility < ch and located above the standard real metric w. r. t. computable reducibility <c. Iterating the construction, we obtain that the ordering (P(ω), ⸦) of subsets of ω is embeddable into the ordering of ch-degrees of real metrics above the standard metric. It is also proved that the countable atomless Boolean algebra is embeddable with preservation of joins and meets into the ordering of c-degrees of computable real metrics.

KW - Cauchy representation

KW - computable analysis

KW - computable metric space

KW - reducibility of representations

KW - representation of real numbers

UR - http://www.scopus.com/inward/record.url?scp=85108859585&partnerID=8YFLogxK

U2 - 10.33048/semi.2021.18.027

DO - 10.33048/semi.2021.18.027

M3 - Article

AN - SCOPUS:85108859585

VL - 18

SP - 377

EP - 392

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

M1 - 29

ER -

ID: 34098139