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Paul
Posts:
406
Registered:
7/12/10


Wikipedia definition of pi system is selfcontradictory  please help me clarify.
Posted:
Jul 9, 2014 7:13 PM


The wikipedia defines a pisystem on a set omega as being a collection P of subsets of omega such that P is nonempty 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 nonempty 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?
Thank You,
Paul Epstein



