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arXiv · 2412.13785

Local reflections of choice

Calliope Ryan-Smith
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Abstract

Under the assumption of small violations of choice with seed $S$ ($\mathsf{SVC}(S)$), the failure of many choice principles reflect to to local properties of $S$, which can be a helpful characterisation for preservation proofs. We demonstrate the reflections of $\mathsf{DC}$, $\mathsf{AC}_\lambda$, $\mathsf{PP}$, and other important forms of choice. As a consequence, we show that if $S$ is infinite then $S$ can be partitioned into $\omega$ many non-empty subsets.

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Calliope Ryan-Smith. 2024-12-18. Local reflections of choice. https://arxiv.org/abs/2412.13785

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