There may be no nowhere dense ultrafilter


We show the consistency of ZFC + ”there is no NWD-ultrafilter on ω”, which means: for every non-principal ultrafilter D on the set of natural numbers, there is a function f from the set of natural numbers to the reals, such that for every nowhere dense set A of reals, {n : f(n) ∈ A} / ∈ D. This answers a question of van Douwen, which was put in more general… (More)


Cite this paper

@inproceedings{Shelah1998ThereMB, title={There may be no nowhere dense ultrafilter}, author={Saharon Shelah}, year={1998} }