Geometric Axioms for Differentially Closed Fields with Several Commuting Derivations
Omar Leon Sanchez
TL;DR
This paper develops a geometric first-order axiomatization for differentially closed fields with multiple commuting derivations, extending previous work to a more complex differential algebraic setting.
Contribution
It introduces a new geometric axiomatization for such fields using a relative prolongation concept, advancing the understanding of their model theory.
Findings
Provides a formal axiomatization in the spirit of Pierce-Pillay.
Extends the theory to multiple commuting derivations.
Uses a relative notion of prolongation for Kolchin-closed sets.
Abstract
A geometric first-order axiomatization of differentially closed fields of characteristic zero with several commuting derivations, in the spirit of Pierce-Pillay, is formulated in terms of a relative notion of prolongation for Kolchin-closed sets.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Polynomial and algebraic computation · Advanced Theoretical and Applied Studies in Material Sciences and Geometry