---
tag: XW1CGTMDYD
kind: concept
name: Stratified
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section S
    note: adopted
    mention: wikipedia://en/43580500#3JY5
    sections: [Summary]
inventory: [8FENGZX2BX]
---

## 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 $\sigma(x) = \sigma(y)$.