Mgr. Jan Starý, Ph.D.

Článek

10.14712/1213-7243.2015.123

Katedra aplikované matematiky

We introduce the notion of a coherent P-ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a P-point on the set of natural numbers, and show that these ultrafilters exist generically under the assumption that the dominating number is not less than the continuum. This improves the known existence result of Ketonen. Similarly, the existence theorem of Canjar can be extended to show that coherently selective ultrafilters exist generically under c = cov(meager). We use these ultrafilters in a topological application: a coherent P-ultrafilter on an algebra B is an untouchable point in the Stone space of B, witnessing its nonhomogeneity.