Hereditarily countable set explained

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]

See also

• Hereditarily finite set
• Constructible universe

Notes and References

1. https://www.jstor.org/pss/2273380 "On Hereditarily Countable Sets"