Failure of an higher analogue of Mho

Ido Feldman

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arXiv · 2407.18603

Failure of an higher analogue of Mho

Ido Feldman

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Abstract

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.

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BibTeX RIS

Ido Feldman. 2024-07-26. Failure of an higher analogue of Mho. https://arxiv.org/abs/2407.18603

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