what even is a halting oracle then if we can't in principle experience one? They seem to be formally useful...
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I'll have to think about whether that satisfies. I'm not sure whether the fact that this TM doesn't show that anything...
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doesn't halt is a problem
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Of course, this only works for Delta^0_2. The arithmetical hierarchy goes a lot higher.
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after thinking, my main problem with your suggestions is that they are two different mathematical objects...
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you can't replace one with the other in proofs, though maybe you'd be able to adapt the proofs
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I'm not sure what you mean. What are the two mathematical objects?
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Subset of N which are codes for TMs that halt vs TM that runs TMs until they halt and output 1 at that code
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Infinite string of 1s is different from TM that writes inf string of 1s, but you suggested using latter to represent former.
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