Standard

Topologies, Ranks, and Closures for Families of Theories. I. / Markhabatov, N. D.; Sudoplatov, S. V.

In: Algebra and Logic, Vol. 59, No. 6, 01.2021, p. 437-455.

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

Harvard

Markhabatov, ND & Sudoplatov, SV 2021, 'Topologies, Ranks, and Closures for Families of Theories. I', Algebra and Logic, vol. 59, no. 6, pp. 437-455. https://doi.org/10.1007/s10469-021-09620-4

APA

Markhabatov, N. D., & Sudoplatov, S. V. (2021). Topologies, Ranks, and Closures for Families of Theories. I. Algebra and Logic, 59(6), 437-455. https://doi.org/10.1007/s10469-021-09620-4

Vancouver

Markhabatov ND, Sudoplatov SV. Topologies, Ranks, and Closures for Families of Theories. I. Algebra and Logic. 2021 Jan;59(6):437-455. doi: 10.1007/s10469-021-09620-4

Author

Markhabatov, N. D. ; Sudoplatov, S. V. / Topologies, Ranks, and Closures for Families of Theories. I. In: Algebra and Logic. 2021 ; Vol. 59, No. 6. pp. 437-455.

BibTeX

@article{ded81da697ad43898f8825d4a3d8b90d,
title = "Topologies, Ranks, and Closures for Families of Theories. I",
abstract = "We describe topological properties, ranks, closures, and their dynamics for families of theories. Types of topologies for families of theories are characterized. A relationship is established between ranks and topologies for families of theories. Boolean combinations of s-definable families of theories are treated, ranks and degrees with respect to these families are found, and values of the characteristics in question are described. We study closures of families of theories with respect to s-definable subfamilies and their Boolean combinations, properties of closure operators, and also a condition for the existence of a least generating set. Rank values for families of theories are specified in terms of algebras of definable subfamilies.",
keywords = "closure, family of theories, rank, topology",
author = "Markhabatov, {N. D.} and Sudoplatov, {S. V.}",
note = "Funding Information: Supported by RFBR (project No. 20-31-90003), by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002), and by KN MON RK (grant No. AP08855497). Publisher Copyright: {\textcopyright} 2021, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jan,
doi = "10.1007/s10469-021-09620-4",
language = "English",
volume = "59",
pages = "437--455",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Topologies, Ranks, and Closures for Families of Theories. I

AU - Markhabatov, N. D.

AU - Sudoplatov, S. V.

N1 - Funding Information: Supported by RFBR (project No. 20-31-90003), by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002), and by KN MON RK (grant No. AP08855497). Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1

Y1 - 2021/1

N2 - We describe topological properties, ranks, closures, and their dynamics for families of theories. Types of topologies for families of theories are characterized. A relationship is established between ranks and topologies for families of theories. Boolean combinations of s-definable families of theories are treated, ranks and degrees with respect to these families are found, and values of the characteristics in question are described. We study closures of families of theories with respect to s-definable subfamilies and their Boolean combinations, properties of closure operators, and also a condition for the existence of a least generating set. Rank values for families of theories are specified in terms of algebras of definable subfamilies.

AB - We describe topological properties, ranks, closures, and their dynamics for families of theories. Types of topologies for families of theories are characterized. A relationship is established between ranks and topologies for families of theories. Boolean combinations of s-definable families of theories are treated, ranks and degrees with respect to these families are found, and values of the characteristics in question are described. We study closures of families of theories with respect to s-definable subfamilies and their Boolean combinations, properties of closure operators, and also a condition for the existence of a least generating set. Rank values for families of theories are specified in terms of algebras of definable subfamilies.

KW - closure

KW - family of theories

KW - rank

KW - topology

UR - http://www.scopus.com/inward/record.url?scp=85103088096&partnerID=8YFLogxK

U2 - 10.1007/s10469-021-09620-4

DO - 10.1007/s10469-021-09620-4

M3 - Article

AN - SCOPUS:85103088096

VL - 59

SP - 437

EP - 455

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 28201756