David Fernández Bretón: Gruff ultrafilters in the Random model

Thursday, January 28, 4:00-5:30 PM at CC Little 2502 (note the nonstandard building/room!!!):

A gruff ultrafilter (a concept introduced by van Douwen) is an ultrafilter on the rational numbers with a base of perfect subsets (where perfect means both closed (in the topology inherited from the usual Euclidean one from the reals) and crowded (without isolated points)). The main question regarding these objects is whether one can prove their existence in ZFC.Partial progress towards the answer of this question so far includes that their existence follows from cov(M)=c (van Douwen), from b=c (Coplakova-Hart) and holds in Sacks model (Millan) and in Miller’s model (F.B. and Hrusak). In this talk I will show a very recent piece of further partial progress: a proof that there exists a gruff ultrafilter in the Random model.

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