arXiv Open Access 2025

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

Stefan Hoffelner

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

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math.LO

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Stefan Hoffelner

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Hoffelner, S. (2025). A Universe with a $Δ^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $Π^1_n$-Uniformization. https://arxiv.org/abs/2506.21778

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Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓