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A note on the axiomatisation of real numbers

✍ Scribed by Thierry Coquand; L. Henri Lombardi

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 86 KB
Volume: 54
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710039

No coin nor oath required. For personal study only.

✦ Synopsis

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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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