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

Stefan Hoffelner

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arXiv · 2604.19360

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

Stefan Hoffelner

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Abstract

Assuming the consistency of $\mathsf{ZFC}$, we construct a model of set theory in which the boldface $\mathbf{\Sigma}^1_3$-uniformization property holds, yet the lightface $\Sigma^1_4$-uniformization property fails, separating these two principles for the first time. We also indicate how to create a universe where $\Sigma^1_3$-uniformization holds, but $\Sigma^1_4$-uniformization fails using inner models with large cardinals.

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BibTeX RIS

Stefan Hoffelner. 2026-04-21. On $\boldsymbol{\Sigma}^1_3$- and $\Sigma^1_4$-uniformization. https://arxiv.org/abs/2604.19360

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