Diagonal intersection

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Diagonal intersection is a term used in mathematics, especially in set theory.

If is an ordinal number and is a sequence of subsets of , then the diagonal intersection, denoted by

is defined to be

That is, an ordinal is in the diagonal intersection if and only if it is contained in the first members of the sequence. This is the same as

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

See also[edit]

References[edit]

  • Thomas Jech, Set Theory, The Third Millennium Edition, Springer-Verlag Berlin Heidelberg New York, 2003, page 92.
  • Akihiro Kanamori, The Higher Infinite, Second Edition, Springer-Verlag Berlin Heidelberg, 2009, page 2.

This article incorporates material from diagonal intersection on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.