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Preprint Number 295

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295. Noa Lavi
Some Positivstellensätze in real closed valued fields
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Submission date: 1 February 2011.

Abstract:

The purpose of this paper is to give a generalization of Hilbert's seventeenth problem in real closed valued fields, That is, to give an algebraic characterization, for a definable set, of the set of polynomials which get only non-negative values on it. We give a general characterization of the positive semi-definite polynomials for any definable set with a Ganzstellensatz, and we also give a representation of those polynomials in the sense of Hilbert 17th problem (that is, in terms of sums of squares) for definable sets from a certain kind.

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