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 admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic equipped with a generic differential-automorphism is elementary; i.e., DCFA exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCFA.
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}
}