Generic derivations on algebraically bounded structures

Abstract

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

Changes: Addded or updated the following references: [FT24] [LM16] [LT24], [JY23b] Corrected the text of Fact 2. Minor typos