Abstract:
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 $\aleph_0$-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.
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