Definition:Rank (Set Theory)

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Definition

Let $A$ be a set.

Let $V$ denote the von Neumann hierarchy.


Then the rank of $A$ is the smallest ordinal $x$ such that $A \in V \left({x+1}\right)$, given that $x$ exists.


Notation

The rank of the class $A$ is sometimes denoted as $\operatorname{rank} \left({A}\right)$.


Also see


Sources