Diagonal intersection

Diagonal intersection is a term used in mathematics

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. This is the same as

$\bigcap _{\gamma <\alpha }([0,\gamma ]\cup S_{\gamma })\,$

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

See also

• Fodor's lemma
• Club set
• Club filter

diagonal intersection at PlanetMath.