The theory DCF$_p$A exists for $p>0$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911189688123392 |
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| author | Ino, Kai Sanchez, Omar Leon |
| author_facet | Ino, Kai Sanchez, Omar Leon |
| contents | We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic $p$ equipped with a generic differential-automorphism is elementary; i.e., DCF$_p$A exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCF$_0$A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The theory DCF$_p$A exists for $p>0$ Ino, Kai Sanchez, Omar Leon Logic 12H05, 12H10, 03C10, 03C60 We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic $p$ equipped with a generic differential-automorphism is elementary; i.e., DCF$_p$A exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCF$_0$A. |
| title | The theory DCF$_p$A exists for $p>0$ |
| topic | Logic 12H05, 12H10, 03C10, 03C60 |
| url | https://arxiv.org/abs/2410.17892 |