Les automorphismes d'un ensemble fortement minimal

Abstract

AbstractLet be a countable saturated structure, and assume that D(v) is a strongly minimal formula (without parameter) such that is the algebraic closure of D(). We will prove the two following theorems:Theorem 1. If G is a subgroup of Aut() of countable index, there exists a finite set A in such that every A-strong automorphism is in G.Theorem 2. Assume that G is a normal subgroup of Aut() containing an element g such that for all n there exists X ⊆ D() such that Dim(g(X)/X) > n. Then every strong automorphism is in G.