diff options
Diffstat (limited to 'sections')
| -rw-r--r-- | sections/conj_classes.tex | 8 | ||||
| -rw-r--r-- | sections/introduction-pl.tex | 2 | ||||
| -rw-r--r-- | sections/introduction.tex | 2 |
3 files changed, 7 insertions, 5 deletions
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. |