The model companion of differential fields with free operators
Omar Leon Sanchez, Rahim Moosa
TL;DR
This paper establishes the existence of a model companion for the theory of differential fields with free operators, extending differential algebra with new lifting techniques.
Contribution
It proves the existence of a model companion for differential fields with free operators, introducing a differential Hensel's Lemma for local finite algebras.
Findings
Existence of a model companion for the theory of differential fields with free operators.
Development of a differential Hensel's Lemma for local finite algebras.
Extension of model theory in differential algebra with new lifting methods.
Abstract
A model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T. Scanlon, Model theory of fields with free operators in characteristic zero, Preprint 2013]. The proof relies on a new lifting lemma in differential algebra: a differential version of Hensel's Lemma for local finite algebras over differentially closed fields.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Mathematical and Theoretical Analysis