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"Core Java" is, essentially JSE, and since JEE (there are no 2's anymore) won't run without the JSE, I must say yes.
Wanting expertise in "Core Java" simply means actually being able to program effectively in Java. If the developer is able to do web and/or enterprise development effectively using JEE, he can certainly program "Core Java". (S)He may not like taking that "step back", but do it, (s)he definately should be able to do.
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