Positivstellens\"atze for semi-algebraic sets in real closed valued   fields
  The purpose of this paper is to give a characterization for polynomials and rational functions which admit only non-negative values on definable sets in real closed valued fields. That is, generalizing the relative positivstellens\"atze for sets defined also by valuation terms. For this, we use model theoretic tools, together with existence of canonical valuations. 
Noa Lavi
math.AG math.LO