Criterion for binarity of -categorical weakly o-minimal theories

Pillay and Steinhorn have described all ℵ 0 -categorical o-minimal theories [A. Pillay, C. Steinhorn, Definable sets in ordered structures I, Transactions of the American Mathematical Society 295 (1986) 565–592]. Their description implies binarity for these theories. Here we present a criterion for binarity of ℵ 0 -categorical weakly o-minimal theories in terms of convexity rank.