  In this note a natural strengthening of internality motivated by complex
geometry, being "Moishezon" to a set of types, is introduced. Under the
hypothesis of Pillay's canonical base property, and using results of
Chatzidakis, a criterion is given for when a finite U-rank stationary type that
is internal to a nonmodular minimal type is in fact Moishezon to the set of all
nonmodular minimal types. This result is a model-theoretic analogue of (a
special case of) Campana's "first algebraicity criterion". Other related
abstractions from complex geometry, including "coreductions" and "generating
fibrations" are also discussed.
