Generic derivations, differential largeness, and NTP$_2$
Elliot Kaplan, Christoph Kesting
TL;DR
This paper explores the relationship between generic derivations and differential largeness in algebraically bounded structures, showing their equivalence in certain cases and preserving NTP$_2$ properties under generic derivation expansion.
Contribution
It establishes the equivalence of genericity and differential largeness for ez-fields and demonstrates that NTP$_2$ structures remain NTP$_2$ after adding a generic derivation.
Findings
Genericity and differential largeness coincide for ez-fields.
NTP$_2$ property is preserved under generic derivation expansion.
Comparison of different frameworks of generic derivations in algebraically bounded structures.
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 algebraically bounded structure remains NTP after expanding by a generic derivation.
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