Английская Википедия:Difference hierarchy

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

In set theory, a branch of mathematics, the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets. If Γ is a pointclass, then the set of differences in Γ is <math>\{A:\exists C,D\in\Gamma ( A = C\setminus D)\}</math>. In usual notation, this set is denoted by 2-Γ. The next level of the hierarchy is denoted by 3-Γ and consists of differences of three sets: <math>\{A : \exists C,D,E\in\Gamma ( A=C\setminus(D\setminus E))\}</math>. This definition can be extended recursively into the transfinite to α-Γ for some ordinal α.[1]

In the Borel hierarchy, Felix Hausdorff and Kazimierz Kuratowski proved that the countable levels of the difference hierarchy over Π0γ give Δ0γ+1.[2]

References

Шаблон:Reflist


Шаблон:Settheory-stub