  In this paper we discuss the inclusion ordering on the filters of a filter
algebra, a special type of Metropolis-Rota algeba. Using embeddings into
interval algebras we show that the notion of "untwisted" gives rise to a
congruence relation on the group of g-filters. We also show that there is a
natural reflection operator on the class of filters with an easily definable
enveloping cubic subalgebra.
