\documentclass[../lic_malinka.tex]{subfiles} \begin{document} Model theory is a field of mathematics that classifies and constructs structures with particular properties (particularly those expressible in first order logic). It describes classical mathematical objects in a broader context, abstracts their properties and studies connections between seemingly unrelated structures. This work studies limits of Fraïssé classes with additional combinatorial and categorical properties. Fraïssé classes are frequently used in model theory, both as a source of examples and to analyse particular ``generic'' structures. The notion of Fraïssé class and its limit is due to the French logician Roland Fraïssé. He also introduced the back-and-forth argument, a fundamental model theoretical method in construction of elementarily equivalent structures, upon which Ehrenfeucht-Fraïssé games are based. The prototypical example for this paper is the random graph \ref{definition: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 Hrushovski property and free amalgamation. Perhaps most importantly, the random graph has a so-called generic automorphism (DODAĆ DEFINICJĘ GENERYCZNEGO AUTOMORFIZMU I ZLINKOWAĆ TUTAJ), which was first proved by Truss in \cite{truss_gen_aut}, where he also introduced the term. The key theorem \ref{theorem:generic_aut_general} says that a Fraïssé class with canonical amalgamation and weak Hrushovski property has a generic automorphism. The fact that such an automorphism exists in this case follows from the classical results of Ivanov \cite{ivanov_1999} and Kechris-Rosendal \cite{https://doi.org/10.1112/plms/pdl007}, we show a new way to construct a generic automorphism by expanding the structures of the class by a (total) automorphism and considering limit of such extended Fraïssé class. We achieve this by using the Banach-Mazur games, a well known method in the descriptive set theory, which proves useful in the study of comeagre sets. Finally, we show how this construction of the generic automorphism can be used to deduce some properties of generic automorphisms (see \ref{proposition:fixed_points}, (COŚ JESZCE)). \end{document}