We present a unifying theoretical and algorithmic approach to the
problems to determine all closed sets of a closure operator, to do
this up to isomorphism, and to determine the elements of certain
ideals of a power set. This will be done by generalizing the concept
of closure operators using the interplay of several orders of a power
set. AMS subject cla&katioos (1991). 06A15, 68RXX. Key words.