Valued difference fields and NTP2

TL;DR

This paper proves that certain valued difference fields, including those with non-standard Frobenius automorphisms, are NTP2, extending model-theoretic classification to these algebraic structures.

Contribution

It establishes NTP2 status for valued difference fields with specific automorphisms, generalizing previous results to broader classes of fields.

Findings

The theory of the non-standard Frobenius automorphism on algebraically closed valued fields is NTP2.

Valued difference fields that are sigma-henselian with NTP2 residue and value group are themselves NTP2.

Results apply to both contractive and isometric cases of valued difference fields.

Abstract

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a sigma-henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference group) are NTP2.