Thread: How many sigma algebras?

Hi,
I was thinking about this problem:
We have for example and the question is: how many diffrent (sigma) algebras we may construct?
In this case we can have {empty set, X}, {empty set, X, {A}, {B,C}}, {empty set, X, {B}, {A,C}}, {empty set, X, {C}, {B,A}} and power set. There are 5 possibilities, but what in general case?

This kind of problem is generally quite difficult. The analogous problem for finite topological spaces is unsolved in the general case, and the few particular solutions we do have are quite complicated! If you do find anything though, I'd be interested in knowing.