It is analogous to the polynomial hierarchy, but with NP replaced with PP.
[1][2] More precisely, the zero-th level is C0P = P, and the (n+1)-th level is Cn+1P = PPCnP (i.e., PP with oracle Cn).
[2] Thus: The counting hierarchy is contained within PSPACE.
[2] By Toda's theorem, the polynomial hierarchy PH is entirely contained in PPP,[3] and therefore in C2P = PPPP.
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