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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-09 13:44:59 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-09 13:44:59 +0200
commite55ffead297fd04fe73e5f7bd6d05a151450fb99 (patch)
tree4a173d26144a7b78ae1fd94ff8f2617d20f9efd9 /sections/conj_classes.tex
parentbd01da032991f9671557ef64e23ca684fa6c995a (diff)
Aspelled
Diffstat (limited to 'sections/conj_classes.tex')
-rw-r--r--sections/conj_classes.tex5
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