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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
commitf5708acfd8c521f9c77b18a00b30b05af9d7ceb3 (patch)
tree4f00f099119a95fd6bd38d2cc349a8df10b7a9bb
parent5d9c6289189f7db6f5792c4e7387b807e9557920 (diff)
Added disclaimer
-rw-r--r--lic_malinka.pdfbin497010 -> 497121 bytes
-rw-r--r--sections/conj_classes.tex8
-rw-r--r--sections/introduction-pl.tex2
-rw-r--r--sections/introduction.tex2
4 files changed, 7 insertions, 5 deletions
diff --git a/lic_malinka.pdf b/lic_malinka.pdf
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diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex
index c72fd38..4732e3c 100644
--- a/sections/conj_classes.tex
+++ b/sections/conj_classes.tex
@@ -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 $\Gamma$,
diff --git a/sections/introduction-pl.tex b/sections/introduction-pl.tex
index dca6599..a839164 100644
--- a/sections/introduction-pl.tex
+++ b/sections/introduction-pl.tex
@@ -39,7 +39,7 @@
teorii mnogości.
Opisana konstrukcja generycznego automorfizmu okazuje się pomocna w dowodzeniu
- niektórych własności tego automorfizmu (patrz \ref{proposition:fixed_points}).
+ niektórych własności tego automorfizmu (patrz \ref{corollary:fixed_points}).
W ostatnim rozdziale przytaczamy przykłady klas Fraïsségo ze słabą własnością
Hrushovskiego i kanoniczną amalgamacją oraz charakteryzujemy ich granice
oraz generyczny automorfizm.
diff --git a/sections/introduction.tex b/sections/introduction.tex
index 57b8de1..25b3358 100644
--- a/sections/introduction.tex
+++ b/sections/introduction.tex
@@ -39,7 +39,7 @@
Finally, we show how this construction of the generic automorphism can be
used to deduce some properties of generic automorphisms
- (see \ref{proposition:fixed_points}). In the last section we give examples
+ (see \ref{corollary:fixed_points}). In the last section we give examples
and anti-examples of Fraïssé classes with weak Hrushovski property and
canonical amalgamation, characterize Fraïssé limits and generic automorphism
of these classes.