On $\boldsymbol{\Sigma}^1_3$- and $\Sigma^1_4$-uniformization
Logic
2026-04-22 v1
Abstract
Assuming the consistency of , we construct a model of set theory in which the boldface -uniformization property holds, yet the lightface -uniformization property fails, separating these two principles for the first time. We also indicate how to create a universe where -uniformization holds, but -uniformization fails using inner models with large cardinals.
Cite
@article{arxiv.2604.19360,
title = {On $\boldsymbol{\Sigma}^1_3$- and $\Sigma^1_4$-uniformization},
author = {Stefan Hoffelner},
journal= {arXiv preprint arXiv:2604.19360},
year = {2026}
}