Mathias and Silver forcing parametrized by density
Logic
2021-02-12 v1
Abstract
We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2^\omega to \omega, while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.
Keywords
Cite
@article{arxiv.2102.06009,
title = {Mathias and Silver forcing parametrized by density},
author = {Giorgio Laguzzi and Heike Mildenberger and Brendan Stuber-Rousselle},
journal= {arXiv preprint arXiv:2102.06009},
year = {2021}
}
Comments
29 pages