Imaginaries and invariant types in existentially closed valued differential fields

TL;DR

This paper advances the model theory of valued differential fields by proving elimination of imaginaries, invariant extension property, and metastability, based on a new criterion for definable types density.

Contribution

It establishes elimination of imaginaries and invariant extension property for valued differential fields, and introduces a criterion for definable types density in algebraically closed valued fields.

Findings

Valued differential fields eliminate imaginaries in the geometric language.

They possess the invariant extension property.

The theory is metastable.

Abstract

We answer two open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced by Haskell, Hrushovski and Macpherson and that they have the invariant extension property. These two result follow from an abstract criterion for the density of definable types in enrichments of algebraically closed valued fields. Finally, we show that this theory is metastable.