# Algebra Seminar talk

2019-12-13

Antoine **Mottet** (Univerzita Karlova)*Cores of structures with a Ramsey expansion*

Abstract:

A core is a relational structure whose endomorphisms behave locally as automorphisms. Cores are objects that appear naturally in the study of constraint satisfaction problems, and in this context it is an important question to determine which classes of structures can be reduced to the study of the cores inside them. The class of finite structures is a trivial such example, and the class of countably categorical structures is another (Bodirsky, 2003). In this talk, I will show that the same holds for structures admitting a countably categorical Ramsey expansion. This is joint work with Michael Pinsker.