Imaginaries and invariant types in existentially closed valued differential fields

摘要

We answer three related 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 results 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.