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arXiv · 2009.02209

Forcing the $\Pi^1_3$-Reduction Property and a Failure of $\Pi^1_3$-Uniformization

Stefan Hoffelner
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Abstract

We force over the constructible universe to obtain a model of the $\Pi^1_3$-reduction property, thus lowering the best known large cardinal strength from the existence of $M_1^{\#}$ to just ZFC. In this model the $\Pi^1_3$-uniformization property fails, which separates these two principles for the first time.

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Stefan Hoffelner. 2020-09-04. Forcing the $\Pi^1_3$-Reduction Property and a Failure of $\Pi^1_3$-Uniformization. https://doi.org/10.1016/j.apal.2023.103292

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