2024/01/25 by Piotr Borodulin–Nadzieja, Borodulin-Nadzieja, Piotr, Jonathan Cancino-Manríquez +3 · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Computability, Logic, AI Algorithms
paper · pdf · doi:10.48550/arxiv.2401.14042
We answer in negative the problem if the existence of a P-measure implies the existence of a P-point. Namely, we show that if we add random reals to a certain unique P-point model, then in the resulting model we will have a P-measure but not P-points. Also, we investigate the question if there is a P-measure in the Silver model. We show that rapid filters cannot be extended to a P-measure in the extension by ω product of Silver forcings and that in the model obtained by the product of ω2 many Silver forcings there are no P-measures of countable Maharam type