The relationship between various filter notions on a GL-monoid

The notion of a generalised filter is extended to the setting of a GL-monoi d. It is shown that there exists a one-to-one correspondence between the co llection of generalised fillers on a set X and the collection of strongly s tratified L-filters on X. Specialising to the case where L is the closed un it interval [0, c] viewed as a Heyting algebra, we show that any strongly s tratified [0 ,c]-filter on X can be uniquely identified with a saturated fi lter on I-X with characteristic value c. In this way, the notion of a gener alised filter unifies various filter notions. In particular, necessity meas ures and finitely additive probability measures are specific examples of ge neralised filters. (C) 1999 Academic Press.