# An algebraic characterization of recursively saturated real closed fields

## Karen Lange

### Wellesley College

We (with D’Aquino and Kuhlmann) give a valuation theoretic characterization for a real closed field to be recursively saturated. Previously, Kuhlmann, Kuhlmann, Marshall, and Zekavat gave such a characterization for kappa-saturation, for all infinite cardinals kappa. Our result extends the characterization for a divisible ordered abelian group to be recursively saturated found in some unpublished work of Harnik and Ressayre.

Karen Lange studies computable model theory, with a focus on the computational complexity of various algebraic structures, including graphs, free groups, and homogeneous models, and in particular on the complexity of structures associated with real closed fields. She received her doctorate from the University of Chicago in 2008, under the supervision of Robert Soare, and subsequently was awarded a National Science Foundation Postdoctoral Research Fellowship for study at Notre Dame University. Currently she is Assistant Professor of Mathematics at Wellesley College.