Difference hierarchy

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 formula_1. 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:
formula_2. This definition can be extended recursively into the transfinite to "α"-Γ for some ordinal "α".
In the Borel hierarchy, Felix Hausdorff and Kazimierz Kuratowski proved that the countable levels of the 
difference hierarchy over Π0"γ" give
Δ0"γ"+1.