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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
 | This set theory-related article is a stub. You can help Wikipedia by expanding it. |
| This article needs additional citations for
verification. (March 2024) |
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
|
| This set theory-related article is a stub. You can help Wikipedia by expanding it. |