Forcing the $\Pi^1_3$-Reduction Property and a Failure of $\Pi^1_3$-Uniformization
Logic
2026-04-15 v6
Abstract
We force over the constructible universe to obtain a model of the -reduction property, thus lowering the best known large cardinal strength from the existence of to just ZFC. In this model the -uniformization property fails, which separates these two principles for the first time.
Cite
@article{arxiv.2009.02209,
title = {Forcing the $\Pi^1_3$-Reduction Property and a Failure of $\Pi^1_3$-Uniformization},
author = {Stefan Hoffelner},
journal= {arXiv preprint arXiv:2009.02209},
year = {2026}
}
Comments
30 pages. Corrected last section