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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-05 22:16:39 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-05 22:16:39 +0200
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\documentclass[../lic_malinka.tex]{subfiles}
\begin{document}
- There will be something!
+ 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.
+
+
+
\end{document}