Note on a differential algebra bound
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929620018790400 |
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| author | Jimenez, Léo |
| author_facet | Jimenez, Léo |
| contents | In a recent article, Freitag, Moosa and the author showed that in differentially closed fields of characteristic zero, if two types are nonorthogonal, then their n+3 and m+3 Morley powers are not weakly orthogonal, where n and m are their respective Lascar ranks.
In this short note, we prove that the bound is tight: there are such types with weakly orthogonal n+2 and m+2 Morley powers. The types in question were constructed by Freitag and Moosa as examples of types with degree of nonminimality 2. As interesting as our result are our methods: we rely mostly on Galois theory and some descent argument for types, combined with the failure of the inverse Galois problem over constant parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on a differential algebra bound Jimenez, Léo Logic 03C45, 03C98, 12H05, 12L12 In a recent article, Freitag, Moosa and the author showed that in differentially closed fields of characteristic zero, if two types are nonorthogonal, then their n+3 and m+3 Morley powers are not weakly orthogonal, where n and m are their respective Lascar ranks. In this short note, we prove that the bound is tight: there are such types with weakly orthogonal n+2 and m+2 Morley powers. The types in question were constructed by Freitag and Moosa as examples of types with degree of nonminimality 2. As interesting as our result are our methods: we rely mostly on Galois theory and some descent argument for types, combined with the failure of the inverse Galois problem over constant parameters. |
| title | Note on a differential algebra bound |
| topic | Logic 03C45, 03C98, 12H05, 12L12 |
| url | https://arxiv.org/abs/2412.06034 |