Abstract

It is shown that in a linearly ordered MV-algebra A , the implication is unique if and only if the identity function is the unique De Morgan automorphism on A . Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A , which is not isomorphic to the original implication