1.  41
    Distributive lattices with an operator.Alejandro Petrovich - 1996 - Studia Logica 56 (1-2):205 - 224.
    It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   4 citations  
  2.  17
    Uniqueness of the implication for totally ordered MV-algebras.Néstor G. Martı́nez & Alejandro Petrovich - 2001 - Annals of Pure and Applied Logic 108 (1-3):261-268.
    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 (...)
    Direct download (4 more)  
    Export citation  
  3.  24
    Editorial Introduction.Manuel Abad & Alejandro Petrovich - 2011 - Studia Logica 98 (1-2):1-3.