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Algebra i logika, 2020, Volume 59, Number 6, Pages 649–679
DOI: https://doi.org/10.33048/alglog.2020.59.603 (Mi al2641) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Topologies, ranks, and closures for families of theories. I

N. D. Markhabatova, S. V. Sudoplatovbca

a Novosibirsk State Technical University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Novosibirsk State University
Full-text PDF (326 kB) Citations (7)
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DOI: https://doi.org/10.33048/alglog.2020.59.603
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: topology, rank, closure, family of theories.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90003
Siberian Branch of Russian Academy of Sciences I.1.1, проект № 0314-2019-0002
Ministry of Education and Science of the Republic of Kazakhstan AP08855497
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).
Received: 22.05.2020
Revised: 05.03.2021
English version:
Algebra and Logic, 2021, Volume 59, Issue 6, Pages 437–455
DOI: https://doi.org/10.1007/s10469-021-09620-4
Bibliographic databases:
Document Type: Article
UDC: 510.67
Language: Russian
Citation: N. D. Markhabatov, S. V. Sudoplatov, “Topologies, ranks, and closures for families of theories. I”, Algebra Logika, 59:6 (2020), 649–679; Algebra and Logic, 59:6 (2021), 437–455
Citation in format AMSBIB
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\by N.~D.~Markhabatov, S.~V.~Sudoplatov
\paper Topologies, ranks, and closures for families of theories.~I
\jour Algebra Logika
\yr 2020
\vol 59
\issue 6
\pages 649--679
\mathnet{http://mi.mathnet.ru/al2641}
\crossref{https://doi.org/10.33048/alglog.2020.59.603}
\transl
\jour Algebra and Logic
\yr 2021
\vol 59
\issue 6
\pages 437--455
\crossref{https://doi.org/10.1007/s10469-021-09620-4}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85103088096}
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    Cycle of papers
    This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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