Diagonal intersection
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
References
- 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.
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