  We conjecture that for a strongly minimal theory T in a finite signature
satisfying the Zilber Trichotomy, there are only three possibilities for the
recursive spectrum of T: all countable models of T are recursively presentable;
none of them are recursively presentable; or only the zero-dimensional model of
T is recursively presentable. We prove this conjecture for disintegrated
(formerly, trivial) theories and for modular groups. The conjecture also holds
via known results for fields. The conjecture remains open for finite covers of
groups and fields.
