ON INVERSE LIMIT OF A PROJECTIVE SYSTEM OF BL-ALGEBRAS

In this paper, the inverse limits of a projective system of basic logic algebras (BL-algebras) are introduced, and their basic properties are studied. The set of congruences of a BL-algebra is considered as a poset. Then, a quotient inverse system and a quotient inverse limit on it are constructed. Moreover, by setting filters of a BL-algebra, quotient projective and inverse systems are constructed.