  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? We prove: (i) The
category of locally finite MV-algebras is not equivalent to any finitary
variety. (ii) More is true: the category of locally finite MV-algebras is not
equivalent to any finitely-sorted finitary quasi-variety. (iii) The category of
locally finite MV-algebras is equivalent to an infinitary variety; with
operations of at most countable arity. (iv) The category of locally finite
MV-algebras is equivalent to a countably-sorted finitary variety.
  Our proofs rest upon the duality between locally finite MV-algebras and the
category of multisets by R. Cignoli, E. J. Dubuc and D. Mundici, and
categorical characterisations of varieties and quasi-varieties proved by J.
Duskin, J. R. Isbell, F. W. Lawvere and others. In fact no knowledge on
MV-algebras is needed, apart from the aforementioned duality.
