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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-24 23:07:30 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-08-24 23:07:30 +0200
commita15a0040023eb4f8f2b9d9653789063b86ccbe62 (patch)
treef14327c8a40e20ce077f1277e3174420c9a7d25e /sections/examples.tex
parent1fb3b8fe52bd8a9edd5121c9b468a015266a4880 (diff)
Extended introducion
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is a Fraïssé class with WHP and CAP.
\end{example}
- The prove of this is relatively easy, knowing that there is essentially one
- vector space of every finite dimension and that every linear independent subset
- of a vector space can be extended to a basis of this space. The Fraïssé limit
- of $\cV$ is the $\omega$-dimensional vector space. Thus, by our key Theorem
- \ref{theorem:key-theorem} we know that it has a generic automorphism.
+ 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