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Diffstat (limited to 'sections/conj_classes.tex')
| -rw-r--r-- | sections/conj_classes.tex | 5 |
1 files changed, 3 insertions, 2 deletions
diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex index 8beace0..3e4cb3a 100644 --- a/sections/conj_classes.tex +++ b/sections/conj_classes.tex @@ -91,7 +91,7 @@ that $\Pi = \Gamma$. We will construct a strategy for the second player in the Banach-Mazur game on the topological space $G$. This strategy will give us a subset - $A\subseteq G$ and as we will see a subset of a cojugacy class in $G$. + $A\subseteq G$ and as we will see a subset of a conjugacy class in $G$. By the Banach-Mazur theorem \ref{theorem:banach_mazur_thm} this will prove that this class is comeagre. @@ -234,6 +234,7 @@ % infinite and has the random graph property. % \end{proof} \begin{proposition} + \label{proposition:fixed_points} Let $\sigma$ be the generic automorphism of $\Gamma$. Then the set of fixed points of $\sigma$ is isomorphic to $\Gamma$. \end{proposition} @@ -242,7 +243,7 @@ Let $S = \{x\in \Gamma\mid \sigma(x) = x\}$. First we need to show that it is an infinite. By the theorem \ref{theorem:generic_aut_general} we know that $(\Gamma, \sigma)$ is the Fraïssé limit of $\cH$, thus we - can embedd finite $L$-structures of any size with identity as an + can embed finite $L$-structures of any size with identity as an automorphism of the structure into $(\Gamma, \sigma)$. Thus $S$ has to be infinite. Also, the same argument shows that the age of the structure is exactly $\cC$. It is weakly ultrahomogeneous, also by the fact that |