  The second major development was Scott’s [1962] application of Rieger-Bernays independence methods to NF. If \(\langle X, E\rangle\) is a binary structure with \(E\) an extensional relation on \(X\) (so that \(\langle X, E\rangle\) is a model of a set theory of some kind) and \(\pi\) is a permutation of \(X\), then \(\{\langle x, \pi(y)\rangle : \langle x, y\rangle \in E\}\) is also an extensional relation on \(X\) and gives us a new model of some kind of set theory. If certain constraints are respected, this method outputs models of ZF when given models of ZF (and was first invented in order to prove the independence of the axiom of foundation from the other axioms of ZF) but it works even better with NF, since the construction preserves stratified formulæ.