Axiom $\mathcal{A}$ and supercompactness
Logic
2024-06-19 v1
Abstract
We produce a model where every supercompact cardinal is -supercompact with inaccessible targets. This is a significant improvement of the main identity-crises configuration obtained in \cite{HMP} and provides a definitive answer to a question of Bagaria \cite[p.19]{Bag}. This configuration is a consequence of a new axiom we introduce -- called -- which is showed to be compatible with Woodin's cardinals. We also answer a question of V. Gitman and G. Goldberg on the relationship between supercompactness and cardinal-preserving extendibility. As an incidental result, we prove a theorem suggesting that supercompactness is the strongest large-cardinal notion preserved by Radin forcing.
Keywords
Cite
@article{arxiv.2406.12776,
title = {Axiom $\mathcal{A}$ and supercompactness},
author = {Alejandro Poveda},
journal= {arXiv preprint arXiv:2406.12776},
year = {2024}
}