Cell decomposition for semi-affine structures on p-adic fields

TL;DR

This paper develops cell decomposition techniques for additive reducts of p-adic fields across various field types, including those with infinite residue fields, without requiring Henselian properties.

Contribution

It introduces a general multi-sorted language approach to cell decomposition applicable to a broad class of p-adic fields, including non-Henselian and infinite residue field cases.

Findings

Cell decomposition results for fields with finite residue fields.

Applicable to non-Henselian p-adic fields.

Works across any characteristic.

Abstract

We use cell decomposition techniques to study additive reducts of p- adic fields. We consider a very general class of fields, including fields with infinite residue fields, which we study using a multi-sorted language. The results are used to obtain cell decomposition results for the case of finite residue fields. We do not require fields to be Henselian, and we allow them to be of any characteristic.