Definable henselian valuations on dp-minimal real fields

TL;DR

This paper characterizes all definable henselian valuations on dp-minimal real fields and identifies conditions under which these fields admit such valuations with real closed residue fields, extending to almost real closed fields.

Contribution

It provides an explicit algebraic characterization of definable henselian valuations on dp-minimal real fields and extends the analysis to almost real closed fields.

Findings

Characterization of all definable henselian valuations on dp-minimal real fields

Identification of dp-minimal real fields with definable henselian valuations with real closed residue fields

Extension of results to almost real closed fields

Abstract

We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue field. We do so by first proving this for the more general setting of almost real closed fields.