Identity crises between supercompactness and Vopenka's Principle

Yair Hayut; Menachem Magidor; Alejandro Poveda

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arXiv · 1905.12289

Identity crises between supercompactness and Vopenka's Principle

Yair Hayut·Menachem Magidor·Alejandro Poveda

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Abstract

In this paper we study the notion of $C^{(n)}$-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 $C^{(1)}$-supercompact but also that the least supercompact is $C^{(1)}$-supercompact (and even $C^{(n)}$-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.

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BibTeX RIS

Yair Hayut, Menachem Magidor, Alejandro Poveda. 2019-05-29. Identity crises between supercompactness and Vopenka's Principle. https://arxiv.org/abs/1905.12289

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