 Independence is demonstrated in exactly the same way. To show that a statement I is independent of a set AX of statements (relative to the consistency of B), one interprets the relevant geometric terms in such a way that the members of AX, as interpreted, express theorems of B, while I expresses the negation of a theorem of B. That is, the independence of I from AX (relative to the consistency of B) is demonstrated by proving the consistency of \(\textit{AX} \cup \{{\sim}I\}\) relative to that of B.