Closed unbounded class of ordinals
= Closed unbounded class of ordinals
= Closed unbounded class
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An unbounded <class in set theory> of <ordinals> is closed if every nonempty set-sized increasing sequence of its members has its supremum in the class. This is the proper-class analogue of a <club set>. The <reflection theorem for definable hierarchies> gives such a class for every finite collection of <first-order formulas>.