Is the category of locally finite MV-algebras equivalent to an equational class?

Abstract: Locally finite MV-algebras form a subclass of MV-algebras which is closed under homomorphic images, subalgebras, and finite products, but not under arbitrary ones. However, the category of locally finite MV-algebras with homomorphisms has arbitrary products in the classical categorical sense. Driven by these considerations, D. Mundici posed the following question: Is the category of locally finite MV-algebras equivalent to an equational class? (D. Mundici. Advanced Lukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235, problem 3.)

We answer this question.

Our proofs rest upon the duality between locally finite MV-algebras and multisets established by R. Cignoli, E. J. Dubuc, and D. Mundici, and categorical characterizations of varieties established by J. Duskin, F. W. Lawvere, and others.

logic

Audience: researchers in the topic

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