English

On $\boldsymbol{\Sigma}^1_3$- and $\Sigma^1_4$-uniformization

Logic 2026-04-22 v1

Abstract

Assuming the consistency of ZFC\mathsf{ZFC}, we construct a model of set theory in which the boldface Σ31\mathbf{\Sigma}^1_3-uniformization property holds, yet the lightface Σ41\Sigma^1_4-uniformization property fails, separating these two principles for the first time. We also indicate how to create a universe where Σ31\Sigma^1_3-uniformization holds, but Σ41\Sigma^1_4-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}
}
R2 v1 2026-07-01T12:28:12.067Z