Generic Derivations on Algebraically Bounded Structures

Abstract

Let ${\mathbb K}$ be an algebraically bounded structure, and let T be its theory. If T is model complete, then the theory of ${\mathbb K}$ endowed with a derivation, denoted by $T^{\delta }$ , has a model completion. Additionally, we prove that if the theory T is stable/NIP then the model completion of $T^{\delta }$ is also stable/NIP. Similar results hold for the theory with several derivations, either commuting or non-commuting.