mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

, a pseudo-intersection of a family of sets is an

infinite set In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Properties The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite. It is the only ...

''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 Fraktur () is a calligraphic hand of the Latin alphabet and any of several blackletter typefaces derived from this hand. The blackletter lines are broken up; that is, their forms contain many angles when compared to the curves of the Anti ...

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

* Set theory {{settheory-stub