Les automorphismes d'un ensemble fortement minimal
Journal of Symbolic Logic 57 (1):238-251 (1992)
| Abstract | Let M be a countable saturated structure, and assume that D(ν) is a strongly minimal formula (without parameter) such that M is the algebraic closure of D(M). We will prove the two following theorems: Theorem 1. If G is a subgroup of $\operatorname{Aut}(\mathfrak{M})$ of countable index, there exists a finite set A in M such that every A-strong automorphism is in G. Theorem 2. Assume that G is a normal subgroup of $\operatorname{Aut}(\mathfrak{M})$ containing an element g such that for all n there exists $X \subseteq D(\mathfrak{M})$ such that $\operatorname{Dim}(g(X)/X) > n$. Then every strong automorphism is in G | |||||||||
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