K. A. Baikalova, D. Yu. Emel'yanov, B. Sh. Kulpeshov, E. A. Palyutin, S. V. Sudoplatov, “On algebras of distributions of isolating formulas of theory of abelian groups and their ordered enrichings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 4, 3–15; Russian Math. (Iz. VUZ), 62:4 (2018), 1

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 4, Pages 3–15 (Mi ivm9344)

This article is cited in 9 scientific papers (total in 10 papers)

On algebras of distributions of isolating formulas of theory of abelian groups and their ordered enrichings

K. A. Baikalova^a, D. Yu. Emel'yanov^b, B. Sh. Kulpeshov^cd, E. A. Palyutin^ebd, S. V. Sudoplatov^deba

^a Novosibirsk State Technical University, 20 K. Marks Ave., Novosibirsk, 630073 Russia
^b Novosibirsk State University, 1 Pirogova str., Novosibirsk, 630090 Russia
^c International Information Technology University, 34A/8A, Manas Zhandosov str., Almaty, 050040 Republic of Kazakhstan
^d Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010 Republic of Kazakhstan
^e Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Ave., Novosibirsk, 630090 Russia

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Abstract: We describe algebras of distributions of binary isolating formulas for theories of abelian groups and their ordered enriching. This description is based on general theory of algebras of isolating formulas and uses the specificity of basedness of theories of abelian groups which is based on Shmeleva's invariants. We give Cayley tables for algebras corresponding to theories of base abelian groups and their ordered enrichings, and point out a machinery of transformation of theories of base abelian groups into algebras for arbitrary theories of abelian groups.

Keywords: algebra of distributions of binary isolating formulas, abelian group, elementary theory, ordered enriching.

Funding agency	Grant number
Ministry of Education and Science of the Republic of Kazakhstan	0830/ГФ4
Russian Foundation for Basic Research	17-01-00531_a
Ministry of Education and Science of the Russian Federation	НШ-6848.2016.1

Received: 13.01.2017

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 4, Pages 1–12
DOI: https://doi.org/10.3103/S1066369X18040011

Bibliographic databases:

Document Type: Article

UDC: 510.670:512.541

Language: Russian

Citation: K. A. Baikalova, D. Yu. Emel'yanov, B. Sh. Kulpeshov, E. A. Palyutin, S. V. Sudoplatov, “On algebras of distributions of isolating formulas of theory of abelian groups and their ordered enrichings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 4, 3–15; Russian Math. (Iz. VUZ), 62:4 (2018), 1–12

Citation in format AMSBIB

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https://www.mathnet.ru/eng/ivm9344

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This publication is cited in the following 10 articles:

B. Sh. Kulpeshov, “Algebry binarnykh formul dlya slabo tsiklicheski minimalnykh teorii s trivialnym opredelimym zamykaniem”, Sib. matem. zhurn., 65:2 (2024), 318–331
Beibut Kulpeshov, Sergey Sudoplatov, “On algebras of binary isolating formulas for weakly circularly minimal theoriesof convexity rank 2”, KMJ, 24:4 (2024), 6
B. Sh. Kulpeshov, “Algebras of binary formulas for $\aleph_0$ -categorical weakly circularly minimal theories: piecewise monotonic case”, Sib. elektron. matem. izv., 20:2 (2023), 824–832
S. V. Sudoplatov, “Arities and aritizabilities of first-order theories”, Sib. elektron. matem. izv., 19:2 (2022), 889–901
B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Non-Trivial Definable Closure”, Lobachevskii J Math, 43:12 (2022), 3532
A. B. Altaeva, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of distributions of binary isolating formulas for almost $\omega$ -categorical weakly $o$ -minimal theories”, Algebra and Logic, 60:4 (2021), 241–262
B. S. Baizhanov, B. Sh. Kulpeshov, T. S. Zambarnaya, “A.D. Taimanov and model theory in Kazakhstan”, Sib. elektron. matem. izv., 17 (2020), 1–58
D. Yu. Emelyanov, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of binary formulas for compositions of theories”, Algebra and Logic, 59:4 (2020), 295–312
D. Emel'yanov, “Algebras of distributions of binary formulas for theories of archimedean solids”, Bull. Irkutsk State Univ.-Ser. Math., 28 (2019), 36–52
D. Yu. Emel'yanov, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of Distributions of Binary Isolating Formulas for Quite $o$ -Minimal Theories”, Algebra and Logic, 57:6 (2019), 429–444

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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