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\begin{document}
Model theory is a field of mathematics that classify and construct
structures with particular properties. It desribes classical mathematical
objects in a broader context, abstract their properties and study
connections between simingly unrelated structures. Roland Fraïssé was
French logician who established many important notions in contemporary
model theory. He was one of the first to utilize back-and-forth argument,
a fundamental model theoretical method in construction of
elementary equivalent structures. The Ehrenfeuht-Fraïssé games is a
concept that proved useful in classical logic, model theory, but also
finite model theory (which is a filed of theoretical informatics rather
than mathematics).
This work study limits of Fraïssé classes with additional combinatorial
and categorical properties. The key theorem \ref{theorem:generic_aut_general}
says that a Fraïssé class with canonical amalgamation and weak Hrushovsky
property has a generic automorphism. This result was known before,
for example [DODAC GDZIE TO BYLO...]. However, we show a new way to construct
a generic automorphism by extending the structures of the class by an
automorphism and considering limit of such extended Fraïssé class. We achieve
this by using the Banach-Mazur games, a well known objects of general topology
which prove useful in study of comeager sets.
The prototype structure of the paper is the random graph (also known as the
Rado graph), the Fraïssé limit of the class of finite undirected graphs.
It serves as a useful example, gives an intuition of the Fraïssé limits,
weak Hrushovsky property and free amalgamation.
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