February 9
Tom Benhamou,
Rutgers University
Tukey-top ultrafilters under UA
In the first part of the talk, we will provide some background and motivation to study the Glavin property. In particular, we will present a recently discovered connection between the Galvin property and the Tukey order on ultrafilters. This is a joint result with Natasha Dobrinen. In the second part, we will introduce several diamond-like principles for ultrafilters, and prove some relations with the Galvin property. Finally, we use the Ultrapower Axiom to characterize the Galvin property in the known canonical inner models. The second and third part is joint work with Gabriel Goldberg.