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
- Hereditarily finite set
- Constructible universe
References
- ^ "On Hereditarily Countable Sets" by Thomas Jech.
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