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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 55

Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure: Monotonic-to-right Case

Author(s)

Aizhan B. Altayeva1,  Beibut Sh. Kulpeshov2,3, Sergey V. Sudoplatov4,5

1 International Information Technology University, Almaty, Kazakhstan

2 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

3 Kazakh British Technical University, Almaty, Kazakhstan

4 Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

5 Novosibirsk State Technical University, Novosibirsk, Russian Federation

Abstract
This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. We consider the binary level of these structures forming algebras of binary isolating formulas, which are based on families of labels and compositions of related formulas. These algebras are studied for ℵ0-categorical 1-transitive non-primitive weakly circularly minimal theories of convexity rank greater than 1 with a trivial definable closure having a non-trivial monotonic-to-right function to the definable completion of a structure. On the basis of the study, the authors present a description of these algebras. It is shown that for this case there exist only commutative algebras. A strict 𝑠-deterministicity of such algebras for some natural number 𝑠 is also established.
About the Authors

Aizhan Bakatkalievna Altayeva, PhD, International Information Technology University, Almaty, 050040, Kazakhstan, vip.altayeva@mail.ru

Beibut Sh. Kulpeshov, Dr. Sci. (Phys.-Math.), Prof., Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan, kulpesh@mail.ru; Kazakh British Technical University, Almaty, 050000, Kazakhstan, b.kulpeshov@kbtu.kz

Sergey V. Sudoplatov, Dr. Sci. (Phys.-Math.), Prof., Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation, sudoplat@math.nsc.ru; Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation, sudoplatov@corp.nstu.ru

For citation
Altayeva A. B., Kulpeshov B. Sh., Sudoplatov S. V. Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure: Monotonic-to-right Case. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 55, pp. 63–79. https://doi.org/10.26516/1997-7670.2026.55.63
Keywords
algebra of binary formulas, ℵ0-categorical theory, weak circular minimality, circularly ordered structure, convexity rank
UDC
510.67
MSC
03C64, 03C07, 03C10, 03C40
DOI
https://doi.org/10.26516/1997-7670.2026.55.63
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