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What impact would a device (ie super-computer or relativistic computer or other method) that solves the halting problem have on math?

Would there be any mathematical problems left to solve?

What would be the greatest mathematical challenges left?

Could we compute if our axiom system is is consistent?

Could we find "the one true and final" complete set theory?

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    The existence of a halting oracle would disprove the Church-Turing thesis. Breaking it open and studying it would lead to new physics since none of the physics we currently have is super-Turing. It would also count as a constructive proof of the law of excluded middle.2011-04-07
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    Why is this tagged [physics]?2011-04-07

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