Diagonal intersection

In mathematics, particularly in set theory, if

$\langle S_{i}\rangle _{i<\alpha }$

is a sequence then the diagonal intersection,

$\Delta _{i<\alpha }S_{i}$

is defined to be

$\{\beta <\alpha \mid \beta \in \bigcap _{\gamma <\beta }S_{\gamma }\}$.

That is, $\beta$ is in $\Delta _{i<\alpha }S_{i}$ if it is contained in the first $\beta$ members of the sequence.

See also: Fodor's lemma, club set, club filter