Suppose L is a signature of continuous first order logic for metric structures and we have a class C of L-structures which we want to investigate from the point of view of model theory. In general, this involves letting T be the L-theory of C, and working to understand the models of T as fully as possible. This means not only knowing which L-structures are models of T, but also understanding the definable predicates and (especially important) the definable sets in models of T. A valuable byproduct could be an explicit axiomatization of T.

In this talk we will lay out how understanding ultraproducts of members of C can be an important practical tool for understanding the full class of models of T. Some examples will be worked out.

A set of beamer slides covering more than can be presented in a seminar talk is posted at https://faculty.math.illinois.edu/~henson/ (scroll down to find the link and some references)