Kreisel and Sacks showed that relativized computability contexts admit c.e. sets whose Turing degree structure diverges from the unrelativized case, undermining the generality of K's completeness claim.
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Turing degree(as a measure of computational difficulty)
A way of measuring how 'hard' a problem is to solve—two problems have the same Turing degree if they're equally difficult from a computational standpoint.
Unrelativized case(as the baseline framework)
The standard, basic situation where no extra tools or shortcuts are allowed—just the pure, fundamental rules of what computation can do.