The logic Ł•

Abstract

The algebraic category MV•is the image of MV, the category whose objects are the MV-algebras, by theequivalenceK•(cf. [7, 8]). In this paper we define the logic Ł•whose Lindenbaum algebra is an MV•-algebra(object of MV•), and establish a link between Ł•and the infinite valued Łukasiewicz logic Ł. We definecU-operators, that have properties of universal quantifiers, and establish a bijection that maps an MV-algebraendowed with a U-operator (cf. [20–22]) into an MV•-algebra endowed with acU-operator. This map extendsto a functor that is a categorical equivalence.