- Equations for formally real meadows
- Journal of Applied Logic
- Volume | Issue number
- 13 | 2, B
- Number of pages
- Document type
- Faculty of Science (FNWI)
Amsterdam University College (AUC)
- Informatics Institute (IVI)
We consider the signatures Σm = (0,1,−,+,⋅,−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 these completeness results in order to obtain complete axiomatizations of the complex numbers.
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