Tameness Properties in Multiplicative Valued Difference Fields with Lift and Section

TL;DR

This paper establishes relative quantifier elimination for a class of multiplicative valued difference fields with a lifting map, and extends NIP transfer results to NTP2, linking model-theoretic properties of these fields to their value group and residue field.

Contribution

It proves quantifier elimination for Pal's valued difference fields with a lifting map and generalizes NIP transfer to NTP2, connecting model-theoretic properties of fields, value groups, and residue fields.

Findings

Proves relative quantifier elimination for Pal's valued difference fields.

Extends NIP transfer results to NTP2 for valued difference fields.

Shows NTP2 property holds iff both value group and residue field are NTP2.

Abstract

We prove relative quantifier elimination for Pal's multiplicative valued difference fields with an added lifting map of the residue field. Furthermore, we generalize a $\mathrm{NIP}$ transfer result for valued fields by Jahnke and Simon to $\mathrm{NTP}_2$ to show that said valued difference fields are $\mathrm{NTP}_2$ if and only if value group and residue field are.