From 37bb95dea0ac896d9c409fe64f3c1ce99ca43bb2 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Wed, 24 Aug 2022 23:22:12 +0200
Subject: Fixes

---
 sections/conj_classes.tex | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

(limited to 'sections/conj_classes.tex')

diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex
index 87fa416..e795217 100644
--- a/sections/conj_classes.tex
+++ b/sections/conj_classes.tex
@@ -85,9 +85,10 @@
 	Let $\cC$ be a Fraïssé class of finitely generated $L$-structures. 
 	Let $\cD$ be the class of structures from $\cC$ with additional unary 
 	function symbol interpreted
-	as an automorphism of the structure. If $\cC$ has the weak Hrushovski property
-	and $\cD$ is a Fraïssé class, then there is a comeagre conjugacy class in the
-	automorphism group of the $\Flim(\cC)$.
+	as an automorphism of the structure. If $\cC$ has the weak Hrushovski 
+	property, $\cD$ is a Fraïssé class and $(\Pi, \sigma) = \Flim(\cD)$, then
+	$\Aut(\cC)$ has a comeagre conjugacy class and $\sigma$ is in this class
+	(i.e. $\sigma$ is a generic automorphism).
   \end{theorem}
 
   Before we get to the proof, it is important to mention that an isomorphism 
@@ -97,7 +98,7 @@
   of finitely generated structures (if it yields one) and \textit{vice versa}. 
 
   \begin{proof}
-	Let $\Gamma = \Flim(\cC)$ and $(\Pi, \sigma) = \Flim(\cD)$. First, by the Theorem
+	Let $\Gamma = \Flim(\cC)$. First, by the Theorem
 	\ref{theorem:isomorphic_fr_lims}, we may assume without the loss of generality
 	that $\Pi = \Gamma$. Let $G = \Aut(\Gamma)$,
 	i.e. $G$ is the automorphism group of $\Gamma$.
@@ -228,7 +229,10 @@
   \begin{theorem}
 	\label{theorem:key-theorem}
 	Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with WHP
-	and canonical amalgamation. Then $\Flim(\cC)$ has a generic automorphism.
+	and canonical amalgamation. Let $\cD$ be the class of structures from $\cC$ with 
+	additional unary function symbol interpreted as an automorphism of the structure.
+	Then $\cD$ is a Fraïssé class and for $(\Pi, \sigma) = \Flim(\cD)$ 
+	we have that the conjugacy class of $\sigma$ is comeagre in $\Aut(\cC)$.
   \end{theorem}
 
   \begin{proof}
-- 
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