# Pseudo-intersection

In mathematical set theory, a **pseudo-intersection** of a family of sets is an infinite set *S* such that each element of the family contains all but a finite number of elements of *S*. The **pseudo-intersection number**, sometimes denoted by the fraktur letter 𝔭, is the smallest size of a family of infinite subsets of the natural numbers that has the strong finite intersection property but has no pseudo-intersection.

## References

- Kunen, Kenneth (2011),
*Set theory*, Studies in Logic,**34**, London: College Publications, ISBN 978-1-84890-050-9, MR 2905394, Zbl 1262.03001

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