In mathematics, specifically set theory, a cumulative hierarchy is a family of sets
such that Some authors additionally require that
[citation needed] The union
of the sets of a cumulative hierarchy is often used as a model of set theory.
[citation needed] The phrase "the cumulative hierarchy" usually refers to the von Neumann universe, which has
A cumulative hierarchy satisfies a form of the reflection principle: any formula in the language of set theory that holds in the union
of the hierarchy also holds in some stages