Series: Penn State Logic Seminar Date: Tuesday, October 7, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: John Clemens, Penn State, Mathematics Title: Distance Sets of Polish Metric Spaces Abstract: A Polish metric space is a separable, complete metric space. The distance set of the metric space is the set of all distances between pairs of points in the space. I will first characterize which sets of real numbers can be the set of distances of some Polish metric space. I will then consider how close the distance set is to being a complete invariant for isometry of Polish metric spaces, and discuss how the theory of definable equivalence relations can be used to show that, in general, it is very far from being a complete invariant.