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diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex index c72fd38..4732e3c 100644 --- a/sections/conj_classes.tex +++ b/sections/conj_classes.tex @@ -242,17 +242,19 @@ \subsection{Properties of the generic automorphism} + This key theorem yields some corollaries and we present one of them below. + Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with weak Hrushovski property and canonical amalgamation. Let $\cD$ be the Fraïssé class (by the Theorem \ref{theorem:key-theorem} of the structures of $\cC$ with additional automorphism of the structure). Let $\Gamma = \Flim(\cC)$. - \begin{proposition} - \label{proposition:fixed_points} + \begin{corollary} + \label{corollary:fixed_points} Let $\sigma$ be the generic automorphism of $\Gamma$. Then the set of fixed points of $\sigma$ is isomorphic to $\Gamma$. - \end{proposition} + \end{corollary} \begin{proof} Let $S = \{x\in \Gamma\mid \sigma(x) = x\}$. It is a substructure of $\Gamma$, |