  MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz
infinite-valued logic, or as unit intervals [0,u] of lattice-ordered abelian
groups in which a strong order unit u>0 has been fixed. They form an equational
class, and the free n-generated free MV-algebra is representable as an algebra
of piecewise-linear continuous functions with integer coefficients over the
unit n-dimensional cube. In this paper we show that the automorphism group of
such a free algebra contains elements having strongly chaotic behaviour, is the
sense that their duals are measure-theoretically isomorphic to a Bernoulli
shift. This fact is noteworthy from the viewpoint of algebraic logic, since it
gives a distinguished status to Lebesgue measure as an averaging measure on the
space of valuations. As an ergodic theory fact, it provides explicit examples
of volume-preserving homeomorphisms of the unit cube which are piecewise-linear
with integer coefficients, preserve the denominators of rational points, and
enjoy the Bernoulli property.
