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出典:『Wikipedia』 (2010/04/26 13:40 UTC 版)

英語による解説

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In set theory, a set is called hereditarily countable if and only if it is a countable set of hereditarily countable sets. This inductive definition is in fact well-founded and can be expressed in the language of first-order set theory. A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable. If the axiom of countable choice holds, then a set is hereditarily countable if and only if its transitive closure is countable.