How strong is a Reinhardt set over extensions of CZF?
2021
Online
report
We investigate the lower bound of the consistency strength of $\mathsf{CZF}$ with Full Separation $\mathsf{Sep}$ and a Reinhardt set, a constructive analogue of Reinhardt cardinals. We show that $\mathsf{CZF+Sep}$ with a Reinhardt set interprets $\mathsf{ZF^-}$ with a cofinal elementary embedding $j\colon V\prec V$. We also see that $\mathsf{CZF+Sep}$ with a Reinhardt set interprets $\mathsf{ZF^-}$ with a model of $\mathsf{ZF+WA_0}$, the Wholeness axiom for bounded formulas.
Comment: 16 pages. Merged into arXiv:2204.05831
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How strong is a Reinhardt set over extensions of CZF?
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Autor/in / Beteiligte Person: | Jeon, Hanul |
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Veröffentlichung: | 2021 |
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