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Positivstellensatz for semi-algebraic sets in real closed valued fields


Author: Noa Lavi
Journal: Proc. Amer. Math. Soc. 143 (2015), 4479-4484
MSC (2010): Primary 03C60, 03C64, 03C98, 12D15, 14P05
DOI: https://doi.org/10.1090/proc/12595
Published electronically: April 29, 2015
MathSciNet review: 3373946
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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 Positivstellensatz for sets defined also by valuation terms. For this, we use model theoretic tools, together with existence of canonical valuations.


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Additional Information

Noa Lavi
Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
Email: noa.lavi@mail.huji.ac.il

DOI: https://doi.org/10.1090/proc/12595
Received by editor(s): October 15, 2013
Received by editor(s) in revised form: April 20, 2014, and July 8, 2014
Published electronically: April 29, 2015
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2015 American Mathematical Society

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