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An Independent Axiom System for the Real Numbers

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Abstract:

We give an irredundant axiomatization of the complete ordered field of real numbers. In particular, we show that all the field axioms for multiplication with the exception of the distributive property may be deduced as theorems in our system. We also provide a complete proof that the axioms we have chosen are independent.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/193113409X469505

Publication date: March 1, 2009

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