The definable multiplicity property and generic automorphisms

Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T ∪ {“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T ∪ {“σi is an automorphism” : i = 1, 2} is an elementary class if and only if T has the definable multiplicity property.