in 2003, Komjoth 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 V��n�nen and Velickovic on games related to Shelah�s logic $L^1_\kappa$, 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 Komj�th-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.
To join this webinar, please send an email to r.zoghi@gmail.com.