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 {" 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 {"i is an automorphism" : i = 1, 2} is an elementary class if and only if T has the definable multiplicity property.

• Type: Journal
• Year: 2000
• Where: APAL
• Authors: Hirotaka Kikyo, Anand Pillay
• Keywords: APAL 2000, Definable Multiplicity Property, Existentially Closed, Strongly Minimal Theory