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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.10698 |
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| _version_ | 1866915432854716416 |
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| author | Jeon, Hanul |
| author_facet | Jeon, Hanul |
| contents | In this paper, we provide a positive answer to the question of Matthews whether $\mathsf{ZF}^-$ is consistent with a non-trivial cofinal Reinhardt elementary embedding $j\colon V\to V$. The consistency follows from $\mathsf{ZFC} + I_0$, and more precisely, it is witnessed by Schlutzenberg's model of $\mathsf{ZF}$ with an elementary embedding $k\colon V_{λ+2}\to V_{λ+2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a cofinal Reinhardt embedding without Powerset Jeon, Hanul Logic 03E55, 03E35, 03E30, 03E70 In this paper, we provide a positive answer to the question of Matthews whether $\mathsf{ZF}^-$ is consistent with a non-trivial cofinal Reinhardt elementary embedding $j\colon V\to V$. The consistency follows from $\mathsf{ZFC} + I_0$, and more precisely, it is witnessed by Schlutzenberg's model of $\mathsf{ZF}$ with an elementary embedding $k\colon V_{λ+2}\to V_{λ+2}$. |
| title | On a cofinal Reinhardt embedding without Powerset |
| topic | Logic 03E55, 03E35, 03E30, 03E70 |
| url | https://arxiv.org/abs/2406.10698 |