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

Алгебры бинарных формул для слабо циклически мини-мальных теорий с тривиальным определимым замыканием: случай монотонности вправо
Altayeva A.B. Kulpeshov B.S. Sudoplatov S.V.
2026 Irkutsk State University

Bulletin of Irkutsk State University, Series Mathematics
2026 #55 63 - 79 pp.

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 N0-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.

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

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International Information Technology University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Kazakh British Technical University, Almaty, 050000, Kazakhstan
Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation
Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation

International Information Technology University
Institute of Mathematics and Mathematical Modeling
Kazakh British Technical University
Sobolev Institute of Mathematics SB RAS
Novosibirsk State Technical University

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