# University Seminar- Computability, Complexity, and Algebraic Structure:Smaller Ultraproducts: A Survey

Time: Wednesday, October 2, 2:20 – 3:20pm

Place: Rome Hall, Room 352

Speaker: Henry Klatt, GWU

Title: Smaller Ultraproducts: A Survey

Abstract: The ultraproduct is a central figure in many fields of logic, most noticeably model theory and set theory. It is formed by taking the space of functions from a set *X* to some structure *M*, and taking the quotient with respect to a notion of largeness called an ultrafilter. While their scale, scope, and power is difficult to overstate, there are unfortunate features of this construction. They are in general quite large, and inherently non-constructive. In this talk, we will present a survey of ultraproduct type constructions, with particular focus on those of interest to computability theory.