  We propose the notion of a quasiminimal abstract elementary class (AEC). This
is an AEC satisfying four semantic conditions: countable
L\"owenheim-Skolem-Tarski number, existence of a prime model, closure under
intersections, and uniqueness of the generic orbital type over every countable
model. We exhibit a correspondence between Zilber's quasiminimal pregeometry
classes and quasiminimal AECs: any quasiminimal pregeometry class induces a
quasiminimal AEC (this was known), and for any quasiminimal AEC there is a
natural functorial expansion that induces a quasiminimal pregeometry class. We
show in particular that the exchange axiom is redundant in Zilber's definition
of a quasiminimal pregeometry class.
