Hereditarily countable set

In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.

The inductive definition above is well-founded and can be expressed in the language of first-order set theory.

A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable.

This set theory-related article is a stub.

You can help Wikipedia by expanding it.