A note on the axiomatisation of real numbers | Zendy

Coquand Thierry | Zendy; Lombardi L. Henri | Zendy

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A note on the axiomatisation of real numbers

Author(s) -

Coquand Thierry,

Lombardi L. Henri

Publication year - 2008

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200710039

Subject(s) - dedekind cut , mathematics , constructive , axiom , forcing (mathematics) , relation (database) , real number , function (biology) , discrete mathematics , constructive proof , calculus (dental) , topos theory , pure mathematics , algebra over a field , mathematical analysis , computer science , medicine , art , geometry , literature , dentistry , process (computing) , database , evolutionary biology , biology , operating system

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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