Failure of an higher analogue of Mho
Logic
2024-07-29 v1
Abstract
Justin Moore's weak club-guessing principle admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of the continuum hypothesis by Inamdar and Rinot. Here we prove that the stronger one may consistently fail. Specifically, starting with a supercompact cardinal and an inaccessible cardinal above it, we devise a notion of forcing consisting of finite working parts and finitely many two types of models as side conditions, to violate this analog of at the second uncountable cardinal.
Cite
@article{arxiv.2407.18603,
title = {Failure of an higher analogue of Mho},
author = {Ido Feldman},
journal= {arXiv preprint arXiv:2407.18603},
year = {2024}
}