... q. Otherwise p and q are incompatible.In the special case of a Boolean algebra, p and q are compatible if and only if p ∧ q = 0.In a tree, however, p and q are compatible if and only if they ... 1, and r is repre-sented in the notationr=rNrN−1 ···r0.r−1r−2 ···.For example, the base of the standard decimalsystem is 10 and we need the digits 0, 1, 2, 3,4, 5, 6, 7, 8, and ... collection of open sets and 01the closed sets. Then for 1 <α<ω1, A∈0αif and only ifA=∪n∈NAnwhere, for each n∈N, An∈0αn and αn<α.A set B is in 0α if and only if the...