**April 29**

Andreas Blass,
University of Michigan

**Do these ultrafilters exist, II: not Tukey top**

This is the second of two talks devoted to two properties of ultrafilters (non-principal, on omega) for which the question 'Do such ultrafilters exist?' is open. In this talk, I'll discuss the property of not being at the top of the Tukey ordering (of ultrafilters on omega). I'll start with the definition of the Tukey ordering, and I'll give an example of an ultrafilter that is 'Tukey top'. It's consistent with ZFC that some ultrafilters are not Tukey top. The examples and the combinatorial characterizations involved here are remarkably similar but not identical to examples and the characterization from the previous talk. That observation suggests some conjectures, one of which I'll disprove if there's enough time.