Expanding Quasi-MV Algebras by a Quantum Operator

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.