The wikipedia defines a pi-system on a set omega as being a collection P of subsets of omega such that P is non-empty and such that A intersect B belongs to P whenever A and B belong to P.
However, the article goes on to give another definition that contradicts the previous one -- namely "That is, P is a non-empty family of subsets of omega that is closed under finite intersections."
These are different definitions. The empty intersection of subsets of omega = omega. Therefore the set omega is required to belong to P under the second definition, but need not do so under the first definition.
Does anyone know whether omega is required to belong to P or is the definition not completely standardised?