  Let $(K,\nu)$ be a real closed valued field, and let $S\subseteq K^n$ be a
definable open semi-algebraic set. We find an algebraic characterization of
rational functions which are OVF-integral on $S$. We apply the existing model
theoretic framework for proving ganzstellens\"atze, and need to control
semi-sections and their relations to orderings. (joint work with Noa Lavi)

Logic