Equations for formally real meadows
| Authors | |
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| Publication date | 29-01-2014 |
| Number of pages | 24 |
| Publisher | Ithaca, NY: ArXiv |
| Organisations |
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| Abstract | 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. |
| Document type | Working paper |
| Note | Also other versions from 2013-2015 available on arXiv.org |
| Language | English |
| Related publication | Equations for formally real meadows |
| Published at | https://arxiv.org/abs/1310.5011v2 |
| Downloads |
1310.5011v2
(Submitted manuscript)
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