Abstract
We give a proof of Grilliot's unpublished theorem that all sets definable by a $\Sigma^1_1$ induction on $\mathbb{N}$ are also definable by a positive $\Sigma^1_1$ induction on $\mathbb{N}$. The proof is recursion-theoretic and likely very similar to Grilliot's original proof.
Citation
Juan P. Aguilera. Ferre Vanden Kerchove. "A Proof of Grilliot's Theorem." Bull. Belg. Math. Soc. Simon Stevin 31 (1) 1 - 16, april 2024. https://doi.org/10.36045/j.bbms.221123a
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