Algebras of binary formulas for ℵ0-categorical weakly circularly minimal theories: monotonic case
DOI:
https://doi.org/10.31489/2024m1/112-127Keywords:
circularly ordered structure, binary formula, isolating formula, algebra of formulas, ℵ0-categorical theory, weak circular minimality, convexity rank, automorphism group, transitivity, primitiveness, m-deterministicityAbstract
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.