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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.13785 |
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| _version_ | 1866909535070846976 |
|---|---|
| author | Ryan-Smith, Calliope |
| author_facet | Ryan-Smith, Calliope |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local reflections of choice Ryan-Smith, Calliope Logic 03E25 (Primary), 03E10 (Secondary) 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. |
| title | Local reflections of choice |
| topic | Logic 03E25 (Primary), 03E10 (Secondary) |
| url | https://arxiv.org/abs/2412.13785 |