Article contents
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.
MSC classification
- Type
- Article
- Information
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1288.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1289.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1290.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1291.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1292.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220612125420425-0313:S0022481220000328:S0022481220000328_inline1293.png?pub-status=live)
- 2
- Cited by