Can you help me understand the class of problems solvable by a nondetermimistic Turing machine with an oracle for SAT running in polynomial time?



How can one characterize NP^SAT?
Surely this class, being $\text{NP}^\text{NP}$, is by definition equal to $\Sigma\_2^p$. In particular, if the Polynomial Hierarchy (PH) does not collapse, then it does not contain $\Pi\_2^p$.


