I'm trying to show that the following problem is undecidable: The intersection between a Context Free Language (CFL) and a Context Sensitive Language(CSL) is the empty set. I know that is undecidable if a CSL is the empty set, but how can I reduce the above problem to this one?
I thought that in according to Chomsky's hierarchy CFL are contained in CSL and CSL are a class of languages closed to intersection. But if I took $\Sigma^*$ i.e. all the possible combination of the alphabet $\Sigma$ as a CSL it would be decidable if it were or not the empty set. So this proof seems wrong to me.