Year: 2026
Type: article
Abstract: Generalising the uniform companion for large fields with a single derivation, we construct a theory of fields of characteristic 0 with free operators—operators determined by a homomorphism from the field to its tensor product with , a finite‐dimensional ‐algebra—which is the model companion of any theory of a field with free operators whose associated difference field is difference large and model complete. Under the assumption that is a local ring, we show that simplicity is transferred from the theory of the underlying field to the theory of the field with operators, and we use this to study the model theory of bounded, PAC fields with free operators.
DOI: 10.1112/jlms.70455
Author: Shezad Mohamed
Institution: University of Manchester
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130441617