# Marek Bienias: About universal structures and Fraisse theorem

Tuesday, April 24, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Marek Bienias (Łódź University of Technology)

Title: About universal structures and Fraisse theorem

Abstract:

For a given structure D of language L we can consider age of D, i.e. the family of all finitely generated L-substructures od D. It turns out that age has property (HP) and (JEP). Fraisse theorem let us revers the procedure: if K is nonempty countable family of finitely generated L-structures having properties (HP), (JEP) and (AP), then there exists exactly one (up to isomorphism) L-structure D (so called Fraisse limit) which is countable ultrahomogenous and has age K.
The aim of the talk is to define basic notions from Fraisse theory, proof the main theorem and show some alternative way of looking at the construction of Fraisse limit.