MV-algebras: a variety for magnitudes with archimedean units
نویسندگان
چکیده
Chang’s MV-algebras are, on the one hand, the algebras of the infinite-valued Lukasiewicz calculus and, on the other hand, they are categorically equivalent to abelian lattice-ordered groups with a distinguished strong unit, for short, unital `-groups. The latter are a modern mathematization of the time-honored euclidean magnitudes with an archimedean unit. While for magnitudes the unit is no less important than the zero element, its archimedean property is not even definable in first-order logic. This gives added interest to the equivalent representation of unital `-groups via the equational class of MV-algebras. In this paper we survey several applications of this equivalence, and various properties of the variety of MV-algebras.
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