Diagonal intersection

Diagonal intersection is a term used in mathematics, especially in set theory.

If δ is an ordinal number and ⟨ X α ∣ α < δ ⟩ is a sequence of subsets of δ , then the diagonal intersection, denoted by

is defined to be

That is, an ordinal β is in the diagonal intersection Δ α < δ X α if and only if it is contained in the first β members of the sequence. This is the same as

where the closed interval from 0 to α is used to avoid restricting the range of the intersection.