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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.21562 |
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| _version_ | 1866913454080655360 |
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| author | Henney-Turner, Christopher Welch, Philip |
| author_facet | Henney-Turner, Christopher Welch, Philip |
| contents | Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $α$-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the ordinals, and then taking a generic extension by a hyperclass Magidor iteration of Prikry forcings. We then show that such simple mice are themselves elements of $L[\mathsf{Reg}]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Of Mice and Machetes Henney-Turner, Christopher Welch, Philip Logic 03E45, 03E55 Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $α$-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the ordinals, and then taking a generic extension by a hyperclass Magidor iteration of Prikry forcings. We then show that such simple mice are themselves elements of $L[\mathsf{Reg}]$. |
| title | Of Mice and Machetes |
| topic | Logic 03E45, 03E55 |
| url | https://arxiv.org/abs/2407.21562 |