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Algebra i logika, 2020, Volume 59, Number 4, Pages 432–457
DOI: https://doi.org/10.33048/alglog.2020.59.402 (Mi al2625) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Algebras of binary formulas for compositions of theories

D. Yu. Emelyanova, B. Sh. Kulpeshovbc, S. V. Sudoplatovdea

a Novosibirsk State Technical University
b Kazakh-British Technical University
c Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty
d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
e Novosibirsk State University
Full-text PDF (323 kB) Citations (9)
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DOI: https://doi.org/10.33048/alglog.2020.59.402
Abstract: We consider algebras of binary formulas for compositions of theories both in the general case and as applied to $\aleph_0$-categorical, strongly minimal, and stable theories, linear preorders, cyclic preorders, and series of finite structures. It is shown that $e$-definable compositions preserve isomorphisms and elementary equivalence and have basicity formed by basic formulas of the initial theories. We find criteria for $e$-definable compositions to preserve $\aleph_0$-categoricity, strong minimality, and stability. It is stated that $e$-definable compositions of theories specify compositions of algebras of binary formulas. A description of forms of these algebras is given relative to compositions with linear orders, cyclic orders, and series of finite structures.
Keywords: algebra of binary formulas, composition of theories, $e$-definable composition, $\aleph_0$-categorical theory, strongly minimal theory, stable theory, linear preorder, cyclic preorder.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP08855544
Siberian Branch of Russian Academy of Sciences I.1.1, проект № 0314-2019-0002
Russian Foundation for Basic Research 20-31-90004
D. Yu. Emel’yanov is Supported by RFBR (project No. 20-31-90004), by KN MON RK (grant No. AP08855544), and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002). B. Sh. Kulpeshov is Supported by RFBR (project No. 20-31-90004), by KN MON RK (grant No. AP08855544), and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002). S. V. Sudoplatov is Supported by RFBR (project No. 20-31-90004), by KN MON RK (grant No. AP08855544), and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002).
Received: 09.04.2019
Revised: 24.11.2020
English version:
Algebra and Logic, 2020, Volume 59, Issue 4, Pages 295–312
DOI: https://doi.org/10.1007/s10469-020-09602-y
Bibliographic databases:
Document Type: Article
UDC: 510.67
Language: Russian
Citation: D. Yu. Emelyanov, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of binary formulas for compositions of theories”, Algebra Logika, 59:4 (2020), 432–457; Algebra and Logic, 59:4 (2020), 295–312
Citation in format AMSBIB
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\paper Algebras of binary formulas for compositions of theories
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\vol 59
\issue 4
\pages 432--457
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\crossref{https://doi.org/10.33048/alglog.2020.59.402}
\transl
\jour Algebra and Logic
\yr 2020
\vol 59
\issue 4
\pages 295--312
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    • This publication is cited in the following 9 articles:
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    		Алгебра и логика Algebra and Logic
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