Uniqueness of the implication for totally ordered MV-algebras Original Research Article

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 Ohkumaʹs 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.