Известия Иркутского государственного университета: Серия "Математика", Vol 52, Iss 1, Pp 120-136 (2025)

algebra of binary formulas, $\aleph_0$-categorical theory, weak circular minimality, circularly ordered structure, convexity rank, Mathematics, QA1-939

This article concerns the notion of weak circular minimality beinga variant of o-minimality for circularly ordered structures. Algebras of binary isolating formulas are studied for $\aleph_0$-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.