Submission date: 8 October 2012.

Abstract:

We use the model completeness and axiomatisation of the theory of closed ordered differential fields to give a differential version of Dubois' nullstellensatz and Stengle's positivstellensatz for ordered fields.

Mathematics Subject Classification: 03C64, 12J15, 12D15, 12H05

Keywords and phrases: Nullstellensatz, ordered fields, derivations, sums of squares

Full text: published in Mathematical Logic Quarterly.