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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-25 22:58:43 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-25 22:58:43 +0200
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tree4f00f099119a95fd6bd38d2cc349a8df10b7a9bb /sections/conj_classes.tex
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@@ -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 $\Gamma$,