Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination

TL;DR

This paper introduces simplified methods using generalized Taylor formulas to perform quantifier elimination in real closed valued fields, enhancing understanding of constructible sets in real valuative affine spaces.

Contribution

It presents a new, straightforward quantifier elimination algorithm for real closed valued fields based on generalized Taylor formulas.

Findings

Simplified quantifier elimination algorithm for cvfs

Theorems on constructible subsets of real valuative affine space

Enhanced methods for computations in real closed valued fields

Abstract

We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real valuative affine space.