Cell decomposition and definable functions for weak p-adic structures

TL;DR

This paper introduces a cell decomposition framework tailored for weak p-adic structures, enabling analysis of reducts of p-adic fields with limited definability of addition and multiplication.

Contribution

It develops a novel cell decomposition method applicable to weak p-adic structures, expanding tools for their study.

Findings

Established a cell decomposition suitable for weak p-adic structures

Applied the framework to a language with restricted addition

Provided insights into the definability in reducts of p-adic fields

Abstract

We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted addition.