A VALUATION THEORETIC CHARACTERIZATION OF RECURSIVELY SATURATED REAL CLOSED FIELDS

We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization for κ-saturation, for a cardinal $\kappa \ge \aleph _0 $ . Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.