Completeness in Partial Differential Fields
James Freitag
TL;DR
This paper investigates the concept of completeness in partial differential varieties, extending results from ordinary differential fields and establishing a valuative criterion to identify complete varieties using differential algebra and model theory.
Contribution
It generalizes known results from ordinary to partial differential fields and introduces a new valuative criterion for differential completeness.
Findings
Established a valuative criterion for differential completeness
Provided new examples of complete partial differential varieties
Extended results from ordinary to partial differential fields
Abstract
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and use it to give a new class of examples of complete partial differential varieties. We use methods from both differential algebra and model theory.
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Taxonomy
TopicsModel Reduction and Neural Networks · Advanced Control Systems Optimization