Work

Separably differentially closed fields

Year: 2025

Type: article

Abstract: We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several (algebraic and model-theoretic) properties of this class. Among other things, we show that it is an elementary class whose theory we denote SDCF, and its completions are determined by specifying the characteristic p and the differential degree of imperfection ϵ. Furthermore, after adding what we call the differential λ-functions, we prove that the theory SDCFp,ϵℓ admits quantifier elimination, is stable, and prime model extensions exist.

Source: Illinois Journal of Mathematics

DOI: 10.1215/00192082-11831126

Authors: Kai Ino, Omar León Sánchez

Institution: University of Manchester

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Model theory of D-large fields and connections to representation theory.