By "reasonable", I mean an admissible numbering that is computable in polynomial time from a practical format for representing programs.
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For reasonable numberings, the halting problem is RE-complete (and hence hard for any subclass of RE) under polynomial-time reductions.
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sort'em with "SleepSort"-like algorithm
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Huh? I'm talking about decision problems, not sorting problems.
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no, I was just jokingly proposing to number TMs by the number of steps in their execution (+arbitrary inside that class),
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that way all halting TMs are numbered with naturals, and all unhalting - with higher ordinals, solving the halting problem
End of conversation
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