Definition:Well-Founded Set

Definition

Let $S$ be a small class.

Let $\map V x$ denote the von Neumann hierarchy.

Then $S$ is a well-founded set if and only if there is some ordinal $x$ such that $S \in \map V x$.

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 9.11$