Jan Stary: Coherent ultrafilters

Tuesday, January 12, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Jan Stary (Czech Technical University, Prague)

Title: Coherent ultrafilters

Abstract:

The notion of a P-ultrafilter on omega can be straightened in a natural way to the notion of a coherent P-ultrafilter on a complete ccc Boolean algebra. These ultrafilters exist generically under the condition isolated by Ketonen, namely c = d.
Similarly, under the Canjar condition c = cov(Meager), coherently Ramsey ultrafilters can be shown to exist.
Existence of “coherent” versions of other traditional objects is an ongoing programme.
The coherent ultrafilters are relevant in an old topological question: a coherent P-ultrafilter on an algebra B is an untouchable point in the Stone space of B, witnessing its nonhomogeneity.

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