January 2016

Jan Stary: Coherent ultrafilters

Tuesday, January 12, 2016 17:15

Room: D1-215

Jan Stary

Title: Coherent ultrafilters

Abstract. The notion of a P-ultrafilter on \( \omega \)can be stranghtened 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 \( \mathfrak c = d\). Similarly, under the Canjar condition \( {\mathfrak c }= cov(Meager)\), 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 non homogeneity.