Forking independence in differentially closed fields of positive characteristic
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915604053622784 |
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| author | Kowalski, Piotr Sánchez, Omar León Martin-Pizarro, Amador |
| author_facet | Kowalski, Piotr Sánchez, Omar León Martin-Pizarro, Amador |
| contents | We provide a differential-algebraic description of forking independence in the stable theory DCF$_{p,m}$ of differentially closed fields of characteristic $p>0$ with $m$-many commuting derivations. As a by-product of this description, we prove that types over algebraically closed subsets of the real sort are stationary. In addition, we prove that the set of non-zero solutions to the Bernoulli differential equation $x'=x^{p^k+1}$ with $k>0$ is strongly minimal and its geometry is strictly disintegrated, which implies that this set is algebraically independent over $\mathbb{F}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forking independence in differentially closed fields of positive characteristic Kowalski, Piotr Sánchez, Omar León Martin-Pizarro, Amador Logic 03C45, 03C60, 12F10, 12H05 We provide a differential-algebraic description of forking independence in the stable theory DCF$_{p,m}$ of differentially closed fields of characteristic $p>0$ with $m$-many commuting derivations. As a by-product of this description, we prove that types over algebraically closed subsets of the real sort are stationary. In addition, we prove that the set of non-zero solutions to the Bernoulli differential equation $x'=x^{p^k+1}$ with $k>0$ is strongly minimal and its geometry is strictly disintegrated, which implies that this set is algebraically independent over $\mathbb{F}_p$. |
| title | Forking independence in differentially closed fields of positive characteristic |
| topic | Logic 03C45, 03C60, 12F10, 12H05 |
| url | https://arxiv.org/abs/2511.04911 |