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Processes and Structures on Approximation Spaces. / Stukachev, A. I.

In: Algebra and Logic, Vol. 56, No. 1, 01.03.2017, p. 63-74.

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

Harvard

Stukachev, AI 2017, 'Processes and Structures on Approximation Spaces', Algebra and Logic, vol. 56, no. 1, pp. 63-74. https://doi.org/10.1007/s10469-017-9426-9

APA

Stukachev, A. I. (2017). Processes and Structures on Approximation Spaces. Algebra and Logic, 56(1), 63-74. https://doi.org/10.1007/s10469-017-9426-9

Vancouver

Stukachev AI. Processes and Structures on Approximation Spaces. Algebra and Logic. 2017 Mar 1;56(1):63-74. doi: 10.1007/s10469-017-9426-9

Author

Stukachev, A. I. / Processes and Structures on Approximation Spaces. In: Algebra and Logic. 2017 ; Vol. 56, No. 1. pp. 63-74.

BibTeX

@article{0525e348498f4f04b3c4e64416358f8a,
title = "Processes and Structures on Approximation Spaces",
abstract = "We introduce the concept of a computability component on an admissible set and consider minimal and maximal computability components on hereditarily finite superstructures as well as jumps corresponding to these components. It is shown that the field of real numbers Σ-reduces to jumps of the maximal computability component on the least admissible set ℍF(∅). Thus we obtain a result that, in terms of Σ-reducibility, connects real numbers, conceived of as a structure, with real numbers, conceived of as an approximation space. Also we formulate a series of natural open questions.",
keywords = "admissible sets, approximation spaces, computability theory, computable analysis, constructive models, hyperarithmetical computability, REDUCIBILITY, PRESENTABILITY",
author = "Stukachev, {A. I.}",
year = "2017",
month = mar,
day = "1",
doi = "10.1007/s10469-017-9426-9",
language = "English",
volume = "56",
pages = "63--74",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "1",

}

RIS

TY - JOUR

T1 - Processes and Structures on Approximation Spaces

AU - Stukachev, A. I.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We introduce the concept of a computability component on an admissible set and consider minimal and maximal computability components on hereditarily finite superstructures as well as jumps corresponding to these components. It is shown that the field of real numbers Σ-reduces to jumps of the maximal computability component on the least admissible set ℍF(∅). Thus we obtain a result that, in terms of Σ-reducibility, connects real numbers, conceived of as a structure, with real numbers, conceived of as an approximation space. Also we formulate a series of natural open questions.

AB - We introduce the concept of a computability component on an admissible set and consider minimal and maximal computability components on hereditarily finite superstructures as well as jumps corresponding to these components. It is shown that the field of real numbers Σ-reduces to jumps of the maximal computability component on the least admissible set ℍF(∅). Thus we obtain a result that, in terms of Σ-reducibility, connects real numbers, conceived of as a structure, with real numbers, conceived of as an approximation space. Also we formulate a series of natural open questions.

KW - admissible sets

KW - approximation spaces

KW - computability theory

KW - computable analysis

KW - constructive models

KW - hyperarithmetical computability

KW - REDUCIBILITY

KW - PRESENTABILITY

UR - http://www.scopus.com/inward/record.url?scp=85018773802&partnerID=8YFLogxK

U2 - 10.1007/s10469-017-9426-9

DO - 10.1007/s10469-017-9426-9

M3 - Article

AN - SCOPUS:85018773802

VL - 56

SP - 63

EP - 74

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -

ID: 10258019