Mathematical Logic Quarterly 48 (2):297-299 (2002)

We give an intuitionistic axiomatisation of real closed fields which has the constructive reals as a model. The main result is that this axiomatisation together with just the decidability of the order relation gives the classical theory of real closed fields. To establish this we rely on the quantifier elimination theorem for real closed fields due to Tarski, and a conservation theorem of classical logic over intuitionistic logic for geometric theories
Keywords real closed field  proof theory  constructive algebra  ordered field
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DOI 10.1002/1521-3870(200202)48:2
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