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The Relationship Between Various Filter Notions on aGL-Monoid

✍ Scribed by J.Gutiérrez Garcı́a; I.Mardones Pérez; M.H Burton

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
89 KB
Volume
230
Category
Article
ISSN
0022-247X

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✦ Synopsis

The notion of a generalised filter is extended to the setting of a GL-monoid. It is shown that there exists a one-to-one correspondence between the collection of generalised filters on a set X and the collection of strongly stratified L-filters w x on X. Specialising to the case where L is the closed unit interval 0, c viewed as a w x Heyting algebra, we show that any strongly stratified 0, c -filter on X can be uniquely identified with a saturated filter on I X with characteristic value c. In this way, the notion of a generalised filter unifies various filter notions. In particular, necessity measures and finitely additive probability measures are specific examples of generalised filters.

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