Isabel Müller

We prove the existence of a model companion of the two-sorted theory of c-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field sort. Using a new criterion which does not rely on a stationary independence relation, we prove that if the field is NSOP $_1$, then the model companion is NSOP $_4$. We also prove that if the field is algebraically closed, then the model companion is c-NIP.