Vector spaces example finished

1 files changed, 11 insertions, 2 deletions

diff --git a/sections/examples.tex b/sections/examples.tex
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@@ -31,8 +31,17 @@
 
   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.
+  always embed space with smaller dimension into the bigger one. 
+
+  Amalgamation is a little more complex but still comes intuitively. Let $A$,
+  $B$ and $C$ be finitely dimensional vector spaces such that $C = A\cap B$.
+  Thus, we can write that $A = C\oplus C_A$ and $B = C\oplus C_B$. Then let 
+  $D = C_A \oplus C \oplus C_B$ with embedding of $A$ and $B$ into $C_A\oplus C$
+  and $C_B\oplus C$ respectively. This is also canonical amalgamation.
+
+  The Fraïssé limit of $\cV$ is an $\omega$-dimensional vector space (which
+  is easy to see by Theorem \ref{theorem:fraisse_thm}). Hence we can conclude
+  that it has a generic automorphism.
 
   Now we give some anti-examples: