# Algebra Seminar talk

2017-05-19

Michael **Kompatscher***Cores of omega-categorical structures*

Abstract:

Two structures A and B are called homomorphically equivalent if there is is a homomorphism from A to B and vice versa. For a *finite* structure A we call B a core of A, if A and B are homomorphically equivalent and B is minimal with that property. It is not hard to see that up to isomorphism there is a unique core of A, which can also be characterized by the property that all its endomorphisms are automorphisms.

In this talk we discuss how to generalize the concept of cores to structures on

- infinite* domains. We then present a new proof of the fact that every

countable omega-categorical structure is homomorphically equivalent to a unique (model-complete) core.