The theory DCF A exists for p > 0

We prove that the elementary class of differential-difference fields in characteristic <i>p</i> &gt; 0 admits a model companion. In the terminology of Chatzidakis–Pillay [4], this establishes that the class of differentially closed fields of characteristic p, equipped with a generic differential automorphism, is elementary; that is, DCF<sub>p</sub>A exists. Along the way, we also provide alternative first-order axiomatisations for DCF (differentially closed fields) and for DCF<sub>0</sub>A.

Publication Details

Journal
Annals of Pure and Applied Logic
Published
2025-10-08
DOI
https://doi.org/10.1016/j.apal.2025.103661
Primary Topic
Diabetic Foot Ulcer Assessment and Management
Type
article
Field-Weighted Citation Impact
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article

The theory DCF A exists for p > 0

Annals of Pure and Applied Logic
Diabetic Foot Ulcer Assessment and Management
article

The theory DCF A exists for p > 0

article en

Abstract

We prove that the elementary class of differential-difference fields in characteristic <i>p</i> &gt; 0 admits a model companion. In the terminology of Chatzidakis–Pillay [4], this establishes that the class of differentially closed fields of characteristic p, equipped with a generic differential automorphism, is elementary; that is, DCF<sub>p</sub>A exists. Along the way, we also provide alternative first-order axiomatisations for DCF (differentially closed fields) and for DCF<sub>0</sub>A.

Annals of Pure and Applied LogicVol. 177(2)
Industry, innovation and infrastructure
Openalex Percentile: Top 39%
Diabetic Foot Ulcer Assessment and Management
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The theory DCF A exists for p &gt; 0 · Annals of Pure and Applied Logic (2025) | TGRS Research Map | TGRS