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Mr.Pear
Posts:
1
Registered:
9/3/09


Dense chains in Boolean atomic algebra
Posted:
Sep 3, 2009 11:22 AM


I have the following problem. Let A be a Boolean algebra which is uncountable and atomic (that is every element is a supremum of some set of atoms). Let C be an uncountable chain in A w.r.t standard order <=. Is it always possible to construct a subchain C' of C which is dense in C? (D is dense in B iff for all b \in B there is some d \in D such that d<= b).



