Аннотация:

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 piecewise monotonic-to-left function to the definable completion of a structure. On the basis of the study, we present a description of these algebras. It is shown that for this case there exist only non-commutative algebras. A strict $s$-deterministicity of such algebras for some natural number $s$ is also established.