The properties of an ultraproduct of a family of structures depend (sometimes in a subtle way) on the properties of the ultrafilter used to form the ultraproduct. We will review some results of this type, concerning properties such as the cardinality and saturation of ultraproducts.

Note: This seminar will provide some background for Mayanthe Malliaris' forthcoming Appalachian Set Theory workshop on November 5, see workshop web page for details.