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IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE
Published online by Cambridge University Press: 07 September 2020
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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- © The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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