Rob Sullivan (Imperial College London)

Type spaces, Hrushovski constructions and giraffes

The KPT correspondence established a connection between extreme amenability of automorphism groups of first-order structures and Ramsey theory. In this talk, I will consider automorphism groups $\operatorname{Aut}(M)$ which fix points on type spaces $S_n(M)$ via a natural action. We will explore a few examples from a combinatorial perspective, and building on work of Evans, Hubicka and Nesetril, we will see that there is an omega-categorical structure M which does not have any omega-categorical expansion $M'$ with $\operatorname{Aut}(M')$ fixing points on type spaces.