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FWIW, the index set of all TMs that accept the empty language -- $L$ in @Nathaniel's comment -- is indeed not recursive. You can show this by Rice's theorem; see our reference question.
@Kröw Hm, the title of the question and its body are very different. For the body, I think the duplicate link is good. Anyway, since this one is ancient, please open a new question about certificates and I'm sure there will be good answers. :) (We could migrate the one from here over, too, if that's helpful.)
@gnasher729 Not sure why you're posting this comment here and not on an answer focussing on the Master theorem, but anyway. Note that all cases of the master theorem fit the scheme you mention; the difference is the relation between costs for the splitting and solving the subproblems.
