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The Positivstellensatz for definable functions on O-minimal structures

Acquistapace, Francesca and Andradas Heranz, Carlos and Broglia, Fabrizio (2002) The Positivstellensatz for definable functions on O-minimal structures. Illinois Journal of Mathematics, 46 (3). pp. 685-693. ISSN 0019-2082

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Abstract

In this note we prove two Positivstellensatze for definable functions of class C-r, 0 less than or equal to r < &INFIN;, in any o-minimal structure 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,...,f(k) &GE; 0}.

Item Type:Article
Uncontrolled Keywords:Positivstellensatz; definable functions; o-minimal structure; real closed field
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14764
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