Boise Set Theory Seminar, February 2014
Abstract: A topological space is Polish if it is separable and completely metrizable. Since many properties common to the Cantor space $2^\omega$ and the Baire space $\omega^\omega$ generalize to Polish spaces, they are naturally the subject of study in descriptive set theory. Among separable and normal spaces, Choquet characterized the Polish ones as those where the second player has a winning strategy in the so-called Choquet game. In this talk, we will study the generalization of this property to spaces of higher weight, where the Choquet game is replaced by an analogous game of longer length. This is joint work with Philipp Schlicht.