A Criterion for Binarity of Almost $ \omega $-Categorical Weakly $ o $-Minimal Theories

Abstract

Continuing the study of weak $ o $ -minimality, we prove a theorem on the behavior of a definable unary function on the set of realizations of a nonalgebraic 1-type in an arbitrary weakly $ o $ -minimal theory. Under study are the properties of almost $ \omega $ -categorical weakly $ o $ -minimal theories. We find sufficient conditions both for weak orthogonality and orthogonality of any finite family of nonalgebraic 1-types over the empty set. The main result of the paper is a criterion for binarity of almost $ \omega $ -categorical weakly $ o $ -minimal theories.

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