October 16
Athar Abdul-Quader, SUNY Purchase College
Kernels of digraphs and truth classes

I will talk about a recent paper by Jim Schmerl which provides an alternative proof that every resplendent model of PA has a full truth class. The proof, surprisingly, boils down to studying kernels of digraphs. A kernel of a digraph is a set K such that for any a, b in K, (a, b) is not an edge, and for any a not in K, there is some b in K such that (a, b) is an edge. Schmerl shows that one can view the result that resplendent models have full truth classes as a particular instance of the result that resplendent digraphs which have local finite height have kernels.