Adam Morawski: P-measures in models without P-points

Tuesday, October 25, 2022 17:00

Location: room C11-3.11

Speaker:
Adam Morawski

Title: P-measures in models without P-points

Abstract: P-points are ultrafilters in which every decreasing sequence of sets from the filter has a pseudointersection (in a sense an intersection modulo finite sets) in the filter. Quite similarly P-measures (known in the literature as measures with additive property*) are finitely additive probability measures in which every decreasing sequence of sets has a pseudointersection with measure equal to the limit of measures of sets from the sequence.

It is not hard to see that (a characteristic function of) a P-point is a P-measure. However, a question whether the existence of P-measures implies the existence of P-points remains open.

I will talk about current knowledge of the problem including my and Piotr Borodulin-Nadzieja's efforts and results - based on the Silver forcing and its variations.