From 43d8381bf8e71d3418f861bc73a8acafa2f25a10 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Tue, 5 Jul 2022 22:16:39 +0200
Subject: Introduction scratch

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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}
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