For the IPM (Tehran), the lecture Partitions of well-founded trees: Three connections with model theory.
Abstract: in 2003, Komjáth and Shelah proved a partition theorem on scattered order types; these in turn could be understood as partition relations for classes of well-founded trees. Recently, two different kinds of applications of the same partition relation have been used in infinitary logic and in model theory: one by Väänänen and Velickovic on games related to Shelah’s logic , another by Shelah and myself on the “canonical tree” of an AEC (a generalization of the Scott sentence for an abstract elementary class). I will describe the Komjáth-Shelah result in the first part and then narrow in the applications (with more details on the second one, from some recent joint work with Shelah). Time permitting, I will also address other interactions between partition relations and model theoretic issues.