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Reports on Mathematical Logic

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No. 44

Francesco PAOLI, Antonio LEDDA, Roberto GIUNTINI, Hector FREYTES

On some properties of quasi-MV algebras and $\sqrt{^{\prime }}$
quasi-MV algebras
A b s t r a c t. We investigate some properties of two varieties of algebras arising from
quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV
algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et
al. 200+} and tightly connected with fuzzy logic. We establish the finite
model property and the congruence extension property for both varieties; we
characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$
quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$
quasi-MV algebras in terms of algebras of functions; finally, we describe
the structure of free algebras with one generator in both varieties.

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