On the prime whales of a Boolean algebra (Q387432)

If \(B\) is a Boolean algebra and \(x\in B\) then \(U_1(x)\) denotes the set of all elements in the principal order filter \(U(x)\) generated by \(x\) except the largest element 1 of \(B\). A whale is an order ideal that has supremum equal to 1. A whale \(A\) is called prime if for every \(x\in B\) exactly one of the sets \(U_1(x)\) and \(U_1(x')\) is contained in \(A\). Using prime ideals, the author gives an alternative to Stone's representation theorem.