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A ganzstellensatz for semi-algebraic sets in real closed valued fields (1101.3253v3)
Published 17 Jan 2011 in math.LO
Abstract: Let $(K,\nu)$ be a real closed valued field, and let $S\subseteq Kn$ 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)