Hereditarily countable set

A set is called **hereditarily countable** if it is countable, and all of its elements (and their elements, recursively) are also countable. In more formal terms, a set \( A \) is hereditarily countable if: 1. \( A \) is countable. 2. Every element of \( A \) is countable. 3. Every element of every element of \( A \) is countable, and so on.