IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE

Yair Hayut; Menachem Magidor; Alejandro Poveda

doi:10.1017/jsl.2020.32

IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE

Yair Hayut, Menachem Magidor, Alejandro Poveda

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we study the notion of C(n)-supercompactness introduced by Bagaria in [3] 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 that under suitable hypothesis the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis.

Original language	English
Pages (from-to)	626-648
Number of pages	23
Journal	Journal of Symbolic Logic
Volume	87
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2020.32
State	Published - 7 Jun 2022

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Keywords

2020 Mathematics Subject Classification 03Exx 03E50 03E57

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abstract = "In this paper we study the notion of C(n)-supercompactness introduced by Bagaria in [3] 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 that under suitable hypothesis the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis. ",

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IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE

Abstract

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