Hereditarily countable set

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

References

  1. ^ "On Hereditarily Countable Sets" by Thomas Jech.


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