澄清序数

arXiv - MATH - Logic Pub Date : 2024-08-19 DOI:arxiv-2408.10367

Noah Schweber

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引用次数: 0

摘要

我们使用对可容许集的强迫来证明，对于在一个俱乐部$C/subset/omega_1$中的每一个序$\alpha$，都有$\alpha$的副本，使得它们之间的同构在相对于每个副本的完整$Pi^1_1$集的连接中是不可计算的。假定 $\mathsf{V=L}$，这接近于最优；另一方面，假定有大红心，则对每一个射影函数都同样成立（而且更成立）。

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Clarifying ordinals

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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arXiv - MATH - Logic

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