Processing math: 100%

Logic Seminar

Tom BenhamouRutgers University
Commutativity of cofinal types of ultrafilters

Friday, April 19, 2024 - 3:15pm
Malott 205

The Tukey order finds its origins in the concept of Moore-Smith convergence in topology and is especially important when restricted to ultrafilters with reverse inclusion. The Tukey order on ultrafilters over ω was studied intensively by many, but still contains several fundamental unresolved problems. After providing motivation for studying the Tukey order, I will present a recently discovered connection to a parallel study at the realm of measurable cardinals, and explain how different the Tukey order is at that level when compared to the situation on ω.
In the second part of the talk, I will demonstrate how ideas and intuition from ultrafilters over measurable cardinals led to new results at the level of ω and present an essentially new method of constructing Tukey-top ultrafilters using Diamond-like Principles on ω.