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  "body": "\n## Summary\n\nIn set theory, a branch of mathematics, the **difference hierarchy** over a pointclass is a hierarchy of larger pointclasses generated by taking [[differences|0RKF1ZT5JJ]] of sets. If Γ is a pointclass, then the set of differences in Γ is $\\{A:\\exists C,D\\in\\Gamma ( A = C\\setminus D)\\}$. 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: $\\{A : \\exists C,D,E\\in\\Gamma ( A=C\\setminus(D\\setminus E))\\}$. This definition can be extended recursively into the transfinite to *α*-Γ for some [[ordinal|0RDJK7EQYY]] *α*.\n",
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