Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Topologies, Ranks, and Closures for Families of Theories. I. / Markhabatov, N. D.; Sudoplatov, S. V.
в: Algebra and Logic, Том 59, № 6, 01.2021, стр. 437-455.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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