On commutativity of circularly ordered c-o-stable groups

Abstract

A circularly ordered structure is called c-o-stable in λ, if for any subset A of cardinality at most λ and for any cut s there exist at most λ one-types over A that are consistent with s. A theory is called c-o-stable if there exists an infinite λ such that all its models are c-o-stable in λ. In the paper, it is proved that any circularly ordered group, whose elementary theory is c-o-stable, is Abelian.