Intuitively it makes sense that all PSPACE languages are reducible to other PSPACE languages in polynomial space. But how would I go about actually showing this?

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The same way that you show that any problem in P is polytime reducible to any other, or that any decidable language is Turing reducible to any other: solve the problem in the reduction.

Note that the claims (yours in the question and mine above) aren't quite true for many-one reductions, since you can't reduce any other language to $\Sigma^*$ or $\emptyset$ using many-one reductions.

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