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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.13785 |
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- 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 $\mathsf{DC}$, $\mathsf{AC}_λ$, $\mathsf{PP}$, and other important forms of choice. As a consequence, we show that if $S$ is infinite then $S$ can be partitioned into $ω$ many non-empty subsets.