I tried to prove or disprove that pp is closed under cook reductions. anyone has a idea or link to a answer?
closed as unclear what you're asking by David Richerby, Evil, Juho, Tom van der Zanden, Gilles♦ Jul 11 '16 at 12:14
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PH $\subseteq$ PPP is known to hold, so if PP is closed under Cook reductions
then PH $\subseteq$ PPP $\subseteq$ PPPP $\subseteq$ PP . ( PH $\subseteq$ PP is not known to hold.)
If PP = PSPACE then PPPP = PPPSPACE = PSPACE = PP .
( PP ≠ PSPACE is not known to hold.)
See the Counting Hierarchy.