Monomialization of morphisms and p-adic quantifier elimination

TL;DR

This paper presents a simplified proof of Macintyre's Theorem on p-adic quantifier elimination by leveraging a monomialization approach derived from the Weak Toroidalization Theorem, extending its applicability.

Contribution

It introduces a new, streamlined proof of p-adic quantifier elimination using monomialization techniques based on the Weak Toroidalization Theorem.

Findings

Simplified proof of Macintyre's Theorem

Extension of Weak Toroidalization to non-closed fields

Demonstrates monomialization's role in p-adic model theory

Abstract

We give a short proof of Macintyre's Theorem on Quantifier Elimination for the p-adic numbers, using a version of monomialization that follows directly from the Weak Toroidalization Theorem of Abramovich an Karu (extended to non-closed fields).