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

Stefan Hoffelner

doi:10.1016/j.apal.2023.103292

paper

Forcing the $I^_{3}^{1}$ -Reduction Property and a Failure of $I^_{3}^{1}$ -Uniformization

arXiv:2009.02209 · doi:10.1016/j.apal.2023.103292

Abstract

We force over the constructible universe to obtain a model of the $I^_{3}^{1}$ -reduction property, thus lowering the best known large cardinal strength from the existence of $M_{1}^{#}$ to just ZFC. In this model the $I^_{3}^{1}$ -uniformization property fails, which separates these two principles for the first time.

30 pages. Corrected last section

Forcing the I^31​-Reduction Property and a Failure of I^31​-Uniformization

Abstract

Forcing the $I^_{3}^{1}$ -Reduction Property and a Failure of $I^_{3}^{1}$ -Uniformization