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Théories géométriques pour l'algèbre des nombres réels

Abstract : We try to obtain a dynamical theory describing the algebraic properties of the field of real numbers, as complete as possible, in constructive mathematics and without the axiom of dependent choice. This would be a first step towards a constructive version of O-minimal structures. In the present paper, we propose a theory which turns out to be very close from the classical theory of real closed local rings. We present the theory of real closed local rings in a constructive form, as a natural purely equational theory, using the virtual roots functions introduced in a previous work.
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Submitted on : Thursday, April 6, 2017 - 5:44:53 PM
Last modification on : Thursday, December 1, 2022 - 11:00:07 AM
Long-term archiving on: : Friday, July 7, 2017 - 3:30:58 PM


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  • HAL Id : hal-01426164, version 3


Henri Lombardi, Assia Mahboubi. Théories géométriques pour l'algèbre des nombres réels. Contemporary mathematics, 2017, Ordered algebraic structures and related topics, 697, pp.239--264. ⟨hal-01426164v3⟩



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