Definability in differential-henselian monotone fields

TL;DR

This paper investigates the definability properties of differential-henselian monotone fields with additional structure, establishing key theorems that simplify their logical descriptions and demonstrate their NIP status.

Contribution

It proves an Equivalence Theorem for these fields, leading to a relative quantifier reduction and showing they have NIP, advancing understanding of their model-theoretic complexity.

Findings

Establishment of an Equivalence Theorem

Relative quantifier reduction achieved

Proved NIP property for the class of fields

Abstract

This paper is a sequel to [1] and considers definability in differential-henselian monotone fields with c-map and angular component map. We prove an Equivalence Theorem among whose consequences are a relative quantifier reduction and an NIP result.