Diagonal intersection

In mathematics, particularly in set theory, if

$\langle S_i\rangle_{i<\alpha}$

is a sequence then the diagonal intersection,

Δ i < α S i

is defined to be

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

That is, $β$ is in $Δ i < α S i$ if it is contained in the first $β$ members of the sequence.

This article incorporates material from diagonal intersection on PlanetMath, which is licensed under the GFDL.