Ramsey-type theorems in certain NIP theories
University of Notre Dame
In the paper “Crossing patterns of semi-algebraic sets” (J. Combin. Theory Ser. A 111, 2005) Alon et al. showed that families of graphs with the edge relation given by a semialgebraic relation of bounded complexity satisfy a stronger regularity property than arbitrary graphs. In this talk we show that this can be generalized to families of graphs whose edge relation is uniformly definable in a structure satisfying a certain model theoretic property called distality.
This is a joint work with A. Chernikov.