A New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories

We introduce a new version of orthogonality for nonalgebraic 1-types in weakly o-minimal theories, that of almost quite orthogonality. It is stated that the non almost quite orthogonality relation is an equivalence relation. The main result is a criterion for a weakly o-minimal theory of finite convexity rank with 1 < I(T, ω) < 2^ω to have exactly 3^m6^l countable pairwise nonisomorphic models for some nonnegative integers m, l < ω in terms of the orthogonality version presented.