Positivstellensätze for semi-algebraic sets in real closed valued fields
arXiv:1101.5872
Abstract
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 positivstellensätze for sets defined also by valuation terms. For this, we use model theoretic tools, together with existence of canonical valuations.
Accepted for publication in Proceedings of the American Mathematical Society