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Diagonal intersection is a term used in mathematics, especially in set theory.
If δ {\displaystyle \displaystyle \delta } is an ordinal number and ⟨ X α ∣ α < δ ⟩ {\displaystyle \displaystyle \langle X_{\alpha }\mid \alpha <\delta \rangle } is a sequence of subsets of δ {\displaystyle \displaystyle \delta } , then the diagonal intersection, denoted by
is defined to be
That is, an ordinal β {\displaystyle \displaystyle \beta } is in the diagonal intersection Δ α < δ X α {\displaystyle \displaystyle \Delta _{\alpha <\delta }X_{\alpha }} if and only if it is contained in the first β {\displaystyle \displaystyle \beta } members of the sequence. This is the same as