Clarifying ordinals
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910570951737344 |
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| author | Schweber, Noah |
| author_facet | Schweber, Noah |
| contents | We use forcing over admissible sets to show that, for every ordinal $α$ in a club $C\subsetω_1$, there are copies of $α$ such that the isomorphism between them is not computable in the join of the complete $Π^1_1$ set relative to each copy separately. Assuming $\mathsf{V=L}$, this is close to optimal; on the other hand, assuming large cardinals the same (and more) holds for every projective functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clarifying ordinals Schweber, Noah Logic 03D45 (Primary) 03E40, 03E55 (Secondary) We use forcing over admissible sets to show that, for every ordinal $α$ in a club $C\subsetω_1$, there are copies of $α$ such that the isomorphism between them is not computable in the join of the complete $Π^1_1$ set relative to each copy separately. Assuming $\mathsf{V=L}$, this is close to optimal; on the other hand, assuming large cardinals the same (and more) holds for every projective functional. |
| title | Clarifying ordinals |
| topic | Logic 03D45 (Primary) 03E40, 03E55 (Secondary) |
| url | https://arxiv.org/abs/2408.10367 |