1. Introduction
It is common when defining a theory axiomatically to ask whether the chosen axioms (like Euclid's axiom of parallels) are independent. Dependent axioms are superfluous from the point of view of the theory (set of theorems); such redundancies can be removed. Similarly, one speaks of independent sets of equations, or of alternative presentations of algebras. In these cases, one is comparing sets of formulæ based simply on number or total size.