# How can one characterize NP^SAT?

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

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Surely this class, being NP^NP, is by definition equal to Sigma2. In particular, if PH does not collapse, then it does not contain Pi2.

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Yes you are obviously right, I actually got confused with another question I meant to ask instead about P^NP. –  Liron Oct 23 '09 at 23:09