Clarifying ordinals
Abstract
We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.10367
- arXiv:
- arXiv:2408.10367
- Bibcode:
- 2024arXiv240810367S
- Keywords:
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- Mathematics - Logic;
- 03D45 (Primary) 03E40;
- 03E55 (Secondary)