Generic derivations, differential largeness, and NTP$_2$

Abstract: We compare Fornasiero and Terzo's framework of generic derivations on algebraically bounded structures with Le\'on S\'anchez and Tressl's differentially large fields. We show in the case of a single derivation that genericity and differential largeness coincide for \'ez-fields, as introduced by Walsberg and Ye. We also show that an NTP$_2$ algebraically bounded structure remains NTP$_2$ after expanding by a generic derivation.