The theory DCFpA exists for p > 0

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-10-08 DOI:10.1016/j.apal.2025.103661

Kai Ino , Omar León Sánchez

引用次数: 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 [4], this says that the class of differentially closed fields of characteristic p equipped with a generic differential-automorphism is elementary; i.e., DCF_pA exists. Along the way, we provide alternative first-order axiomatisations for DCF (differentially closed fields) and also for DCF₀A.

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理论DCFpA存在于p > 0

我们证明了特征p>；0的微分-差分域（初等）类允许一个模型伴生。在Chatzidakis-Pillay[4]的术语中，这表明具有一般微分自同构的特征p的微分闭域类是初等的；即，DCFpA存在。在此过程中，我们为DCF（差分闭域）和DCF0A提供了备选的一阶公理化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.

The theory DCFpA exists for p > 0

Abstract

The theory DCFpA exists for p > 0