Free Boolean algebra

In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that:

1. Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and
2. The generators are as independent as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in every Boolean algebra no matter which elements are chosen.