Equations for formally real meadows

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چکیده

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Equations for formally real meadows

We consider the signatures Σm = (0, 1,−,+, ·, ) of meadows and (Σm, 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 the...

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ژورنال

عنوان ژورنال: Journal of Applied Logic

سال: 2015

ISSN: 1570-8683

DOI: 10.1016/j.jal.2015.01.004