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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-25 23:08:15 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-25 23:08:15 +0200
commitf45656a556b0918c4c8c4c6077381e29273b62ab (patch)
tree945abb0b754322683f2bb29ab68d8871abf53006 /sections
parentf5708acfd8c521f9c77b18a00b30b05af9d7ceb3 (diff)
Some other issues
Diffstat (limited to 'sections')
-rw-r--r--sections/conj_classes.tex9
-rw-r--r--sections/examples.tex2
2 files changed, 8 insertions, 3 deletions
diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex
index 4732e3c..446b70e 100644
--- a/sections/conj_classes.tex
+++ b/sections/conj_classes.tex
@@ -184,7 +184,6 @@
$(B_{i,j}, \beta_{i,j})$ to $(\Gamma'_n, g'_n)$. But this can be easily
done by the fact, that $\cD$ has the amalgamation property.
-
It is important to note that $g'_n$ should be a finite function and once
again, as it is an automorphism of a finitely generated structure, we may
think it is simply a map from one generators of $\Gamma'_n$ to the
@@ -240,9 +239,15 @@
and the above Theorem \ref{theorem:generic_aut_general}.
\end{proof}
+ \begin{corollary}
+ Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with WHP
+ and canonical amalgamation. Then $\Flim(\cC)$ has a generic automorphism.
+ \end{corollary}
+
\subsection{Properties of the generic automorphism}
- This key theorem yields some corollaries and we present one of them below.
+ The key Theorem \ref{theorem: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.
diff --git a/sections/examples.tex b/sections/examples.tex
index d9101de..438f3cb 100644
--- a/sections/examples.tex
+++ b/sections/examples.tex
@@ -120,7 +120,7 @@
\end{figure}
\vspace{0.5cm}
- On the other hand $\cL$ cannot have $WHP$. This follows from the fact that
+ On the other hand $\cL$ cannot have WHP. This follows from the fact that
that only automorphism of a finite linear ordering is identity, so
we cannot extend a partial automorphism sending exactly one element to
some distinct element. However, in this case, generic automorphism exists