There may be no nowhere dense ultrafilter

by Shelah. [Sh:594]
Proc Logic Colloquium Haifa'95, 1998
We show the consistency of ZFC + ``there is no NWD-ultrafilter on omega'', which means: for every non principle 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 some nowhere dense set A of reals, the set {n: f(n) in A} is not in D . This answers a question of van Douwen, which was put in more general context by Baumgartner

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