Event Detail

Fri Mar 15, 2024
Evans 60
4–6 PM
Logic Colloquium
Tom Benhamou (Rutgers)
Commutativity of cofinal types of ultrafilters

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 the topological motivation for the Tukey order, I will present recent developments in the theory of the Tukey order restricted to ultrafilters on measurable cardinals, and explain how different the situation is when compared to ultrafilters on ω. In the second part of the talk, we will demonstrate how ideas and intuition from ultrafilters over measurable cardinals led to new results at the level of ω.