“PSPACE and EXP are the next two big steps above NP in the complexity hierarchy.
“Then there’s NEXP then EXPSPACE, then EEXP then NEEXP then EEXPSPACE, and so on ad infinitum. Whee!“
They do that in computer science, don’t they? Yeah?
From Jeff Erickson‘s Lecture 21: NP-Hard Problems available at http://drona.csa.iisc.ernet.in/~gsat/Course/DAA/lecture_notes/jeff_nphard.pdf