Dilators and the reverse mathematics zoo
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929308871688192 |
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| author | Freund, Anton |
| author_facet | Freund, Anton |
| contents | A predilator is a particularly uniform transformation of linear orders. We have a dilator when the transformation preserves well-foundedness. Over the theory $\mathsf{ACA}_0$ from reverse mathematics, any $Π^1_2$-formula is equivalent to the statement that some predilator is a dilator. We show how this completeness result breaks down without arithmetical comprehension: over $\mathsf{RCA}_0+\mathsf{PA}$, the statements from a large part of the reverse mathematics zoo are not equivalent to some predilator being a dilator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dilators and the reverse mathematics zoo Freund, Anton Logic 03B30, 05D10, 03F15, 03F35 A predilator is a particularly uniform transformation of linear orders. We have a dilator when the transformation preserves well-foundedness. Over the theory $\mathsf{ACA}_0$ from reverse mathematics, any $Π^1_2$-formula is equivalent to the statement that some predilator is a dilator. We show how this completeness result breaks down without arithmetical comprehension: over $\mathsf{RCA}_0+\mathsf{PA}$, the statements from a large part of the reverse mathematics zoo are not equivalent to some predilator being a dilator. |
| title | Dilators and the reverse mathematics zoo |
| topic | Logic 03B30, 05D10, 03F15, 03F35 |
| url | https://arxiv.org/abs/2404.06872 |