Cumulative hierarchy


In mathematics, specifically set theory, a cumulative hierarchy is a family of sets Wα indexed by ordinals α such that
Some authors additionally require that Wα+1 ⊆ P or that W0 is empty.
The union W of the sets of a cumulative hierarchy is often used as a model of set theory.
The phrase "the cumulative hierarchy" usually refers to the standard cumulative hierarchy Vα of the von Neumann universe with Vα+1 = P introduced by.

Reflection principle

A cumulative hierarchy satisfies a form of the reflection principle: any formula in the language of set theory that holds in the union W of the hierarchy also holds in some stages Wα.

Examples