Title: The Jonsson Problem: An Application of Universal Algebras to Set Theory

Abstract: One way to generalize the common objects of algebra is consider a set closed under at most countably functions, each of which may have a different number of inputs. As in the normal course of things, it is of interest to analyze the subalgebras of such an object. When the underlying set is infinite, it possible for the subalgebras to proper, but still full size. The infinite combinatorics arising from the study of such large subalgebras turns out to have connections to a variety of problems in set theory. In this talk we will develop this bridge between algebra and set theory.