The Automorphism Group of Falsum-Free Product Logic.

A few things are known, and many are unknown, on the automorphism group of the free MV-algebra over n − 1 generators. In this paper we show that this group appears as the stabilizer of ${\rm 1\mskip-4mu l}$ in the larger group of all automorphisms of the free cancellative hoop over n generators. Both groups have a dual action on the same space, namely the (n − 1)-dimensional cube. The larger group has a richer dynamics, at the expense of loosing the two key features of the McNaughton homeomorphisms: preservation of denominators of rational points, and preservation of the Lebesgue measure. We present here some basic results, some examples, and some problems. [ABSTRACT FROM AUTHOR]