Diagonal intersection

In mathematics, particularly in set theory, if

<math>\langle S_i\rangle_{i<\alpha}<math>

is a sequence then the diagonal intersection,

<math>\Delta_{i<\alpha} S_i<math>

is defined to be

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

That is, <math>\beta<math> is in <math>\Delta_{i<\alpha} S_i<math> if it is contained in the first <math>\beta<math> members of the sequence.

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

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