Positivstellensatz for semi-algebraic sets in real closed valued fields
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3373946