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arXiv · 2410.17892

The theory DCF$_p$A exists for $p>0$

Kai Ino·Omar Leon Sanchez
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Abstract

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.

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Kai Ino, Omar Leon Sanchez. 2024-10-23. The theory DCF$_p$A exists for $p>0$. https://arxiv.org/abs/2410.17892

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