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arXiv · 2312.02540

A Failure of $Π^1_{n+3}$-Reduction in the Presence of $Σ^1_{n+3}$-Separation

Stefan Hoffelner
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Abstract

We show that one can force over $L$ that $Σ^1_3$-separation holds, while $Π^1_3$-reduction fails, thus separating these two principles for the first time. The construction can be lifted to canonical inner models $M_n$ with $n$-many Woodin cardinals, yielding that assuming the existence of $M_n$, $Σ^1_{n+3}$-separation can hold, yet $Π^1_{n+3}$-reduction fails.

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Stefan Hoffelner. 2026-04-14. A Failure of $Π^1_{n+3}$-Reduction in the Presence of $Σ^1_{n+3}$-Separation. https://arxiv.org/abs/2312.02540

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