Clarifying ordinals

Noah Schweber

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arXiv · 2408.10367

Clarifying ordinals

Noah Schweber

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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.

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BibTeX RIS

Noah Schweber. 2024-08-19. Clarifying ordinals. https://arxiv.org/abs/2408.10367

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