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Fall 2002 The Positivstellensatz for definable functions on o-minimal structures
F. Acquistapace, C. Andradas, F. Broglia
Illinois J. Math. 46(3): 685-693 (Fall 2002). DOI: 10.1215/ijm/1258130979

Abstract

In this note we prove two Positivstellensätze for definable functions of class $C^r$, $0\le r < \infty$, in any $o$-minimal structure $\mathcal{S}$ expanding a real closed field $R$. Namely, we characterize the definable functions that are nonnegative (resp. strictly positive) on basic definable sets of the form $F=\{f_1\ge 0,\dots, f_k\ge 0\}$.

Citation

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F. Acquistapace. C. Andradas. F. Broglia. "The Positivstellensatz for definable functions on o-minimal structures." Illinois J. Math. 46 (3) 685 - 693, Fall 2002. https://doi.org/10.1215/ijm/1258130979

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1018.03037
MathSciNet: MR1951235
Digital Object Identifier: 10.1215/ijm/1258130979

Subjects:
Primary: 03C64
Secondary: 13J30

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 3 • Fall 2002
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