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.
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:
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.
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