Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that P_(m+1)-tt^SAT = P_m-tt^SAT implies P_btt^SAT = P_m-tt^SAT and for all sets A

• FP_(m+1)-tt^A = FP_m-tt^A implies FP_btt^A = FP_m-tt^A
• P_(m+1)-T^A = P_m-T^A implies P_bT^A = ... more >>>

A recursive enumerator for a function $h$ is an algorithm $f$ which enumerates for an input $x$ finitely many elements including $h(x)$. $f$ is an $k(n)$-enumerator if for every input $x$ of length $n$, $h(x)$ is among the first $k(n)$ elements enumerated by $f$. If there is a $k(n)$-enumerator for ... more >>>