In parallel to the classical Dixmier-Moeglin equivalence (from noncommutative algebra), it is an interesting problem to understand when certain classes of prime ideals in affine complex algebras equipped with a derivation coincide. More precisely, we consider the question: under which circumstances, in such complex algebras, do the differential primitive, differential locally closed, and differential rational ideals coincide? In joint work with Bell, Launois, and Moosa we presented an example where this equivalence does not hold. Recently, with Bell and Moosa, we proved that it does hold when the algebra has a Hopf algebra structure. We used model theory of differential fields to do this.