Series: Penn State Logic Seminar Date: Tuesday, November 30, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: John Clemens, Penn State, Mathematics Title: Classifying ultrahomogeneous metric spaces Abstract: A metric space is said to be ultrahomogeneous if any partial isometry between finite subsets can be extended to an isometry of the whole space. We consider the difficulty of classifying separable, complete ultrahomogeneous metric spaces up to isometry. On the one hand, the collection of isometry types of finite subsets of such a space is a complete isometry invariant among these spaces; however, these collections are quite complicated objects. We will show that certain types of invariants are not sufficient to classify these spaces up to isomtery, in particular the isometry relation on ultrahomogeneous spaces does not admit classification by countable structures.