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Diagonal intersection

In mathematics, particularly in set theory, if

\langle S_i\rangle_{i<\alpha}

is a sequence then the diagonal intersection,

Δi < αSi

is defined to be

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

That is, β is in Δi < αSi if it is contained in the first β members of the sequence.

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

Last updated: 05-30-2005 21:08:03
Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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