David Fernández Bretón: Ultrafilters on the rationals generated by perfect sets

Place: Fields Institute (Room 210)

Date: June 17th, 2016 (13:30-15:00)

Speaker: David Fernandez Bretón

Title: Ultrafilters on the rationals generated by perfect sets

Abstract:  In a 1992 paper, van Douwen defined what he calls a
“gruff ultrafilter”: an ultrafilter on the rational numbers which
is generated by perfect (this is, closed and crowded) sets; and
asked whether these ultrafilters exist, providing in the same
paper a proof that they do if cov(M)=c. The question of whether
the existence of gruff ultrafilters can be proved in ZFC alone
remains open, but further progress has been made in the
way of consistently positive answers. In this talk I will
present a proof that gruff ultrafilters exist in the Random
model, as well as in any model satisfying d=c. Joint work
with Michael Hrusak.

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