Abstract
We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety \(\sqrt{\prime} {\mathbb{QMV}}\) of such \(\sqrt{\prime}\) quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate \(\sqrt{\prime} {\mathbb{QMV}}\) ,we prove a standard completeness theorem for \(\sqrt{\prime} {\mathbb{QMV}}\) w.r.t. an algebra over the complex numbers.
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Giuntini, R., Ledda, A. & Paoli, F. Expanding Quasi-MV Algebras by a Quantum Operator. Stud Logica 87, 99–128 (2007). https://doi.org/10.1007/s11225-007-9079-0
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DOI: https://doi.org/10.1007/s11225-007-9079-0