hereditarily countable set

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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.[https://www.jstor.org/pss/2273380 "On Hereditarily Countable Sets"] by Thomas Jech.

See also

References

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Category:Set theory

Category:Large cardinals

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