Fri Oct 29, 2010
60 Evans Hall, 4:10–6 PM
Isaac Goldbring (Hedrick Assistant Adjunct Professor of Mathematics, UCLA)
A Survey of the Model Theory of Urysohn’s Metric Space
Urysohn’s metric space U is the unique (up to isometry) Polish (i.e. complete, separable) metric space which is universal, that is it contains an isometric copy of all Polish metric spaces, and ultrahomogeneous, that is any isometry between finite subspaces of U extends to an isometry of U. Urysohn’s metric space (and its isometry group) has been studied by topologists and descriptive set theorists for a plethora of reasons. In this talk, I will outline much of what is known on the model theory of Urysohn’s metric space in the context of model theory for metric structures, which I will introduce at the beginning of my talk. I will discuss matters such as axiomatizability, quantifier elimination, independence relations, and definability.