Identity crises between supercompactness and Vopenka's Principle
Logic
2019-05-30 v1
Abstract
In this paper we study the notion of -supercompactness introduced by Bagaria in \cite{Bag} and prove the identity crises phenomenon for such class. Specifically, we show that consistently the least supercompact is strictly below the least -supercompact but also that the least supercompact is -supercompact (and even -supercompact). Furthermore, we prove under suitable hypothesis that the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis.
Cite
@article{arxiv.1905.12289,
title = {Identity crises between supercompactness and Vopenka's Principle},
author = {Yair Hayut and Menachem Magidor and Alejandro Poveda},
journal= {arXiv preprint arXiv:1905.12289},
year = {2019}
}