Felipe Estrada Pelaez (Universidad de Los Andes) – Model Theory of D-sets

Abstract: In this talk I will discuss model-theoretic aspects of colored D-sets. A D-set is a relational structure on the leaves of a tree with a quaternary relation defined such that we have D(x,y,z,w) if and only if the path from x to y is disjoint from the path from z to w. D-sets have been studied in depth by Adeleke and Neumann. I will describe the class of ultrahomogeneous colored D-sets, the classification of their (unbounded) indiscernible sequences, a characterization of distal colored D-sets, and a proof that every colored D-set is monadically NIP. These results are based on joint work with John Goodrick.