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/examples.tex | 63 ++++++++++++++++++++++++++++-----------------------
 1 file changed, 35 insertions(+), 28 deletions(-)

(limited to 'sections/examples.tex')

diff --git a/sections/examples.tex b/sections/examples.tex
index fdb8c6a..3d276ff 100644
--- a/sections/examples.tex
+++ b/sections/examples.tex
@@ -1,6 +1,41 @@
 \documentclass[../lic_malinka.tex]{subfiles}
 
 \begin{document}
+  In this section we give examples and anti-examples of Fraïssé classes
+  with WHP or CAP.
+
+
+  \begin{example}
+	The class of all finite graphs $\cG$ is a Fraïssé class with WHP and free
+	amalgamation.
+  \end{example}
+
+  We have already shown this fact. Thus get that the random graph has a generic
+  automorphism.
+
+  \begin{example}
+	A $K_n$-free graph is a graph with no $n$-clique as its subgraph. 
+	Let $\cG_n$ be the class of finite \emph{$K_n$-free} graphs. $\cG_n$ 
+	is a Fraïssé class with WHP and free amalgamation.
+  \end{example}
+
+  Showing that $\cG_n$ is indeed a Fraïssé class is almost the same as in
+  normal graphs, together with free amalgamation. WHP is trickier and the proof
+  can be seen in \cite{eppa_presentation} Theorem 3.6. Hence, $\Flim(\cG_n)$
+  has a generic automorphism.
+
+  \begin{example}
+	The class $\cV$ of all finitely generated vector spaces over a countable field
+	is a Fraïssé class with WHP and CAP.
+  \end{example}
+
+  Vector spaces of the same dimension are isomorphic, thus it is obvious that
+  $\cV$ is essentially countable. Also $HP$ and $JEP$ are obvious, as we can
+  always embed space with smaller dimension into the bigger one. Amalgamation
+  works exactly the same. In fact, such amalgamation is indeed canonical.
+
+  Now we give some anti-examples:
+
   \begin{example}
 	Let $\cL$ be the class of all finite linear orderings. Then:
 	\begin{enumerate}
@@ -155,32 +190,4 @@
   Thus there cannot be a dense conjugacy class in $\Aut(\Sigma)$ and so there's
   no generic automorphism.
 
-  \begin{example}
-	The class $\cV$ of all finitely generated vector spaces over a countable field
-	is a Fraïssé class with WHP and CAP.
-  \end{example}
-
-  Vector spaces of the same dimension are isomorphic, thus it is obvious that
-  $\cV$ is essentially countable. Also $HP$ and $JEP$ are obvious, as we can
-  always embed space with smaller dimension into the bigger one. Amalgamation
-  works exactly the same. In fact, such amalgamation is indeed canonical.
-
-  \begin{example}
-	The class of all finite graphs $\cG$ is a Fraïssé class with WHP and free
-	amalgamation.
-  \end{example}
-
-  We have already shown this fact. Thus get that the random graph has a generic
-  automorphism.
-
-  \begin{example}
-	A $K_n$-free graph is a graph with no $n$-clique as its subgraph. 
-	Let $\cG_n$ be the class of finite \emph{$K_n$-free} graphs. $\cG_n$ 
-	is a Fraïssé class with WHP and free amalgamation.
-  \end{example}
-
-  Showing that $\cG_n$ is indeed a Fraïssé class is almost the same as in
-  normal graphs, together with free amalgamation. WHP is trickier and the proof
-  can be seen in \cite{eppa_presentation} Theorem 3.6. Hence, $\Flim(\cG_n)$
-  has a generic automorphism.
 \end{document}
-- 
cgit v1.2.3

