On measures induced by forcing names for ultrafilters
Logic
2021-05-13 v1
Abstract
We study the interplay between properties of measures on a Boolean algebra A and forcing names for ultrafilters on A. We show that several well known measure theoretic properties of Boolean algebras (such as supporting a strictly positive measure or carrying only separable measures) have quite natural characterizations in the forcing language. We show some applications of this approach. In particular, we reprove a theorem of Kunen saying that in the classical random model there are no towers of height .
Cite
@article{arxiv.2105.05339,
title = {On measures induced by forcing names for ultrafilters},
author = {Piotr Borodulin-Nadzieja and Katarzyna Cegiełka},
journal= {arXiv preprint arXiv:2105.05339},
year = {2021}
}