On behaviour of 2-formulas in ordered theories with non-maximal number of countable models

Abstract

Here linearly ordered theories being weakly o - minimal are studied. In particular, theories having a nonmaximal countable spectrum are considered. Two - place formulas of which the sets of solutions lie in the set of realizations of a non - algebraic type are studied. An influence of behavior of such formulas on the number of countable pairwise non - isomorphic models has been investigated. We prove that each such formula generates an equivalence relation.