A problem that is in PSPACE but not known to be in PH? As we know Graph Isomorphism is in NP but it is not known to be NP-Complete or P-Complete. I was wondering if there are any problems that are known to be in PSPACE but not known to be PSPACE-Complete and not lie in PH?
The existential theory of the reals is known to be contained in PSPACE, but it is not known whether it is contained in PH. So take the existential theory of the reals, or any of the many equivalent problems.