The Approachability Ideal Without a Maximal Set
Logic
2018-10-26 v3
Abstract
We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously adding partial square sequences on multiple stationary sets. We show that certain quotients of such forcings have the -approximation property. We apply these ideas to prove, assuming the consistency of a greatly Mahlo cardinal, that it is consistent that the approachability ideal does not have a maximal set modulo clubs.
Cite
@article{arxiv.1607.04772,
title = {The Approachability Ideal Without a Maximal Set},
author = {John Krueger},
journal= {arXiv preprint arXiv:1607.04772},
year = {2018}
}