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تسجيل مستخدم جديدEquations for formally real meadows
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We consider the signatures $Sigma_m=(0,1,-,+, cdot, ^{-1})$ of meadows and $(Sigma_m, {mathbf s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.
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