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arXiv · 2510.14821

The Ordering Principle and Higher Dependent Choice

Peter Holy·Jonathan Schilhan
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Abstract

We provide, for any regular uncountable cardinal $\kappa$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<\kappa}$ and the ordering principle in the presence of a failure of the axiom of choice. We also generalise his methods and obtain these consistency results in a larger class of models.

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Peter Holy, Jonathan Schilhan. 2025-10-16. The Ordering Principle and Higher Dependent Choice. https://arxiv.org/abs/2510.14821

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