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arXiv · 2506.21778

A Universe with a $\Delta^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $\Pi^1_n$-Uniformization

Stefan Hoffelner
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Abstract

This paper details the construction of a universe where $\Pi^1_3$-uniformization is true, the Continuum Hypothesis holds yet it possesses a $\Delta^1_3$-definable well-order of its reals. The method can be lifted to canonical inner models with finitely many Woodin cardinals to produce universes of $\mathsf{CH}$, $\Pi^1_n$-uniformization and where additionally a $\Delta^1_n$-definable well-order of the reals exist.

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Stefan Hoffelner. 2025-06-26. A Universe with a $\Delta^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $\Pi^1_n$-Uniformization. https://arxiv.org/abs/2506.21778

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