The event algebra \(\EC\) consists of all projectors formed by taking sums of some of the \(P_j\) in the collection; i.e., \(\sum_j\pi_j P_j\), where each \(\pi_j\) is either 0 or 1. This includes the identity operator \(I\) and the zero operator 0 along with such things as \(P_2\) or \(P_1+P_3\). The event algebra is a Boolean algebra in the sense that the complement \(I-P\) of any projector and the product \(PQ\) of any two projectors belonging to \(\EC\) is an element of \(\EC\). The term framework can refer to either the sample space or the event algebra constructed from it in this way, since there is a one-to-one correspondence between the two. Quantum theory does not in general specify the probability \(p_j\) to be assigned to the projector \(P_j\) in \(\SC\), apart from the requirement that it be nonnegative, and that the \(p_j\) sum to 1 (but see subsection 4.2 concerning time dependence). Thus, for example, to the element \(P_1+P_3\) of \(\EC\) one assigns the probability \(p_1+p_3\). The intuitive interpretation of probabilities introduced in this way is the same as in the other sciences which employ probability theory as long as a single framework is in view. What is distinctly different in the quantum case is the existence of multiple incompatible frameworks; given these consistency requires that one adopt the single framework rule, subsection 3.4.