A Universe with large Continuum, global $\Sigma$-Uniformization and a projective Well-Order of its Reals

Stefan Hoffelner

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arXiv · 2506.12393

A Universe with large Continuum, global $\Sigma$-Uniformization and a projective Well-Order of its Reals

Stefan Hoffelner

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Abstract

We construct a model in which the continuum has size $\kappa$ for a regular cardinal $\kappa$ and in which the $\Sigma^1_n$-uniformization property holds simultaneously for every $n \ge 2$. Additionally this model has a $\Delta^1_3$- definable well-order of its reals.

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BibTeX RIS

Stefan Hoffelner. 2025-06-14. A Universe with large Continuum, global $\Sigma$-Uniformization and a projective Well-Order of its Reals. https://arxiv.org/abs/2506.12393

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