Stratified

Summary

A formula of set theory is stratified if and only if there is a function $\sigma$ which sends each variable appearing in $\phi$ (considered as an item of syntax) to a natural number (this works equally well if all integers are used) in such a way that any atomic formula $x \in y$ appearing in $\phi$ satisfies $\sigma(x)+1 = \sigma(y)$ and any atomic formula $x = y$ appearing in $\phi$ satisfies $\sigma(x) = \sigma(y)$.