Algebras of binary formulas for ℵ0-categorical weakly circularly minimal theories: monotonic case
ℵ0-категориялық әлсiз циклдiк минималды теориялар үшiн бинарлық формулалар алгебралары: монотонды жағдай
Алгебры бинарных формул для ℵ0-категоричных слабо циклически минимальных теорий: монотонный случай
Kulpeshov B.S. Sudoplatov S.V.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#113Issue 1112 - 127 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 countably categorical weakly circularly minimal theories of convexity rank greater than 1 having both a 1-transitive non-primitive automorphism group and a non-trivial strictly monotonic 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 there exist both commutative and non-commutative algebras among these ones. A strict m-deterministicity of such algebras for some natural number m is also established.
algebra of formulas , automorphism group , binary formula , circularly ordered structure , convexity rank , isolating formula , mdeterministicity , primitiveness , transitivity , weak circular minimality , ℵ0-categorical theory
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Institute of Mathematics and Mathematical Modeling, Kazakh-British Technical University, 28 Shevchenko street, Almaty, 050010, Kazakhstan
Algebra and Mathematical Logic, Novosibirsk State Technical University, 4 Academician Koptyug avenu, Novosibirsk, 630090, Russian Federation
Institute of Mathematics and Mathematical Modeling
Algebra and Mathematical Logic
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