Polynomial time truth-table reductions to p-selective sets

We make an elaborate analysis of the intervals defined by the ordered list of queries to the p-selective set. It turns out that the properties we derive are strong enough to get a collapse to P for several complexity classes, assuming that they are quasi-linear truth-table reducible (or in some cases o(logn)-tt reducible) to a p-selective set. More specifically, for any class 𝒦∈{NP, PP, C=P, ⊕P) we show that if 𝒦 is quasi-linear truth-table reducible to a p-selective set then 𝒦=P. For other Mod_kP classes (k>2) we show that if Mod_kP is o(log n)-truth-table reducible to a p-selective set then Mod_kP=P