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Bibliographic Details
Main Author: Feldman, Ido
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.18603
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author Feldman, Ido
author_facet Feldman, Ido
contents Justin Moore's weak club-guessing principle $\mho$ 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 $\mho$ at the second uncountable cardinal.
format Preprint
id arxiv_https___arxiv_org_abs_2407_18603
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Failure of an higher analogue of Mho
Feldman, Ido
Logic
Justin Moore's weak club-guessing principle $\mho$ 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 $\mho$ at the second uncountable cardinal.
title Failure of an higher analogue of Mho
topic Logic
url https://arxiv.org/abs/2407.18603