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arXiv · 2105.05339

On measures induced by forcing names for ultrafilters

Piotr Borodulin-Nadzieja·Katarzyna Cegiełka
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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 $\omega_2$.

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Piotr Borodulin-Nadzieja, Katarzyna Cegiełka. 2021-05-11. On measures induced by forcing names for ultrafilters. https://arxiv.org/abs/2105.05339

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