IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE

Yair Hayut, Menachem Magidor, Alejandro Poveda

Research output: Contribution to journalArticlepeer-review

2 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 languageAmerican English
Pages (from-to)626-648
Number of pages23
JournalJournal of Symbolic Logic
Volume87
Issue number2
DOIs
StatePublished - 7 Jun 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
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Keywords

  • 2020 Mathematics Subject Classification 03Exx 03E50 03E57

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