Hereditarily countable set
Template:Refimprove In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.
Results
The inductive definition above is well-founded and can be expressed in the language of first-order set theory.
Equivalent properties
A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable.[1]