Are locally finite MV-algebras a variety?

We answer Mundici's problem number 3 (D. Mundici. Advanced {\L}ukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equivalent to an equational class? prove: (i) The is not any finitary variety. (ii) More true: finitely-sorted quasi-variety. (iii) infinitary variety; with operations at most countable arity. (iv) a countably-sorted Our proofs rest upon duality between and multisets by R. Cignoli, E. J. Dubuc D. Mundici, categorical characterisations varieties quasi-varieties proved Duskin, Isbell, F. W. Lawvere others. In fact no knowledge on needed, apart from aforementioned duality.