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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». 2025. Vol 52

Algebras of Binary Formulas for Weakly Circularly Minimal Theories: Monotonic-to-left Case

Author(s)
Aizhan B. Altayeva1, Beibut Sh. Kulpeshov2,3

1International Information Technology University, Alma-Ata, Kazakhstan

2Institute of Mathematics and Mathematical Modeling, Alma-Ata, Kazakhstan

3Kazakh-British Technical University, Alma-Ata, Kazakhstan

Abstract

This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. Algebras of binary isolating formulas 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-left function acting on the universe 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 non-commutative algebras. A strict m-deterministicity of such algebras for some natural number m is also established.

About the Authors

Aizhan B. Altayeva, PhD in Mathematics, International Information Technology University, Alma-Ata, 050040, Kazakhstan, vip.altayeva@mail.ru

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

For citation
Altayeva A.B., Kulpeshov B.Sh. Algebras of Binary Formulas for Weakly Circularly Minimal Theories: Monotonic-to-left Case. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 52, pp. 120–136.

https://doi.org/10.26516/1997-7670.2025.52.120

Keywords

algebra of binary formulas, ℵ0-categorical theory, weak circular minimality, circularly ordered structure, convexity rank

UDC
510.67
MSC
03C64, 03C07
DOI
https://doi.org/10.26516/1997-7670.2025.52.120
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