Algebras of Binary Formulas for Weakly Circularly Minimal Theories: Monotonic-to-left Case
Алгебры бинарных формул для слабо циклически минимальных теорий: монотонный влево случай
Altayeva A.B. Kulpeshov B.Sh.
2025Irkutsk State University
Bulletin of Irkutsk State University, Series Mathematics
2025#52120 - 136 pp.
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.
algebra of binary formulas , circularly ordered structure , convexity rank , weak circular minimality , ℵ0-categorical theory
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International Information Technology University, Alma-Ata, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Alma-Ata, 050010, Kazakhstan
Kazakh British Technical University, Alma-Ata, 050000, Kazakhstan
International Information Technology University
Institute of Mathematics and Mathematical Modeling
Kazakh British Technical University
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