# Definition:Supertransitive

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## Definition

Let $A$ be a transitive class.

Then $A$ is said to be a **supertransitive class** iff:

- $\forall x \in A: \mathcal P \left({ x }\right) \subseteq A$

That is, if $A$ contains the power set of all of its elements.

## Sources

- 1971: Gaisi Takeuti and Wilson M. Zaring:
*Introduction to Axiomatic Set Theory*: $\S 9.8$