m 2 ∑ Bτ →hV/Aντ wV/A dNV/A τ
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Multifunction algebras and the provability of PH
We introduce multifunction algebras Bτ i where τ is a set of 0 or 1-ary terms used to bound recursion lengths. We show that if for all ` ∈ τ we have ` ∈ O(|x|) then Bτ i = FP p i−1(wit, τ̇), those multifunctions computable in polynomial time with at most O(p(`(x))) queries to a Σpi−1 witness oracle for ` ∈ τ and p a polynomial. We use our algebras to obtain independence results in bounded arithm...
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