A Note On The Axiomatisation Of Real Numbers

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Mathematical Logic Quarterly 54 (3):224-228 (2008)
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Abstract

Is it possible to give an abstract characterisation of constructive real numbers? A condition should be that all axioms are valid for Dedekind reals in any topos, or for constructive reals in Bishop mathematics. We present here a possible first-order axiomatisation of real numbers, which becomes complete if one adds the law of excluded middle. As an application of the forcing relation defined in [3, 2], we give a proof that the formula which specifies the maximum function is not provable in this theory.

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10.1002/malq.200710039

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