A valuation theoretic characterization of recursively saturated real closed fields

TL;DR

This paper provides a valuation-based criterion to determine when a real closed field is recursively saturated, extending previous work on divisible ordered abelian groups to real closed fields.

Contribution

It introduces a valuation theoretic characterization for recursive saturation in real closed fields, broadening the scope of existing characterizations.

Findings

Valuation theoretic criteria for recursive saturation in real closed fields

Extension of Harnik and Ressayre's characterization to real closed fields

New insights into the structure of recursively saturated real closed fields

Abstract

We give a valuation theoretic characterization for a real closed field to be recursively saturated. Our result extends the characterization of Harnik and Ressayre \cite{hr} for a divisible ordered abelian group to be recursively saturated.