English

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

Logic 2025-10-06 v2

Abstract

We prove that the (elementary) class of differential-difference fields in characteristic p>0p>0 admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic pp equipped with a generic differential-automorphism is elementary; i.e., DCFp_pA exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCF0_0A.

Keywords

Cite

@article{arxiv.2410.17892,
  title  = {The theory DCF$_p$A exists for $p>0$},
  author = {Kai Ino and Omar Leon Sanchez},
  journal= {arXiv preprint arXiv:2410.17892},
  year   = {2025}
}
R2 v1 2026-06-28T19:32:55.402Z