As far as I'm aware, EXPSPACE is the most inclusive computational complexity class. I was wondering if/how people conceptualize supersets of EXPSPACE.
Thinking about this question, I came up with a couple thoughts of my own:
Maybe EXPSPACE = the set of all Recursively Enumerable problems, i.e. $\Delta_1$ in the arithmetical hierarchy. In this case, the rest of the arithmetical hierarchy would come after EXPSPACE.
Maybe there are problems with space requirements that need to be described by non-computatable functions. For example, take the Busy Beaver function, $BB(n)$, which returns the maximum number of steps an $n$-state Turing Machine could take before halting. $BB$ grows faster than any computable function -- so if a problem required $BB(n)$ space to solve, maybe that would put it in a complexity class after EXPSPACE? In other words, maybe after EXPSPACE there is one or more sets of problems that require a non-computable amount of space to solve.