Counting hierarchy

In complexity theory, the counting hierarchy is a hierarchy of complexity classes. It is analogous to the polynomial hierarchy, but with NP replaced with PP. It was defined in 1986 by Klaus Wagner.
More precisely, the zero-th level is C₀P = P, and the -th level is C_n+1P = PP^C_nP. Thus:

C₀P = P
C₁P = PP
C₂P = PP^PP
C₃P = PP^{PP^PP}
...

The counting hierarchy is contained within PSPACE. By Toda's theorem, the polynomial hierarchy PH is entirely contained in P^PP, and therefore in C₂P = PP^PP.