The theory DCFpA exists for p>0
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., DCFpA exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCF0A.
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