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A Duality for (n+1)-valued MV-algebras

Lattanzi M., Petrovich A.

Reports on Mathematical Logic

2009

Vol. 44

65-84

MV -algebras were introduced by Chang to prove the completeness of the infinite-valued Lukasiewicz propositional calculus. In this paper we give a categorical equivalence between the varieties of (n + 1)-valued MV-algebras and the classes of Boolean algebras endowed with a certain family of filters. An- other similar categorical equivalence is given by A. Di Nola and A. Lettieri. Also, we point out the relations between this categor- ical equivalence and the duality established by R. Cignoli, which can be derived from results obtained by P. Niederkorn on natural dualities for varieties of MV -algebras.

(N + 1) - bounded Wajsberg Algebras with a U-operator

Lattanzi M.

Reports on Mathematical Logic

2005

Nr 39

89-111

Wajsberg algebras are just a reformulation of Chang $MV-$algebras where implication is used instead of disjunction. $MV-$algebras were introduced by Chang to prove the completeness of the infinite-valued {\L}ukasiewicz propositional calculus. Bounded Wajsberg algebras are equivalent to bounded $MV-$algebras. The class of (n+1)-bounded Wajsberg algebras endowed with a $U-$operator, which plays the role of the universal quantifier, is studied. The simple algebras and the subalgebras of the finite simple algebras are characterized. It is proved that this variety of algebras is semisimple and locally finite.