Algebras of binary formulas for ℵ0-categorical weakly circularly minimal theories: monotonic case

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 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.

Keywords

• circularly ordered structure
• binary formula
• isolating formula
• algebra of formulas
• ℵ0-categorical theory
• weak circular minimality