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Can Turing machines capture everything we can compute?

Bhupinder Singh Anand
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Abstract

If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are not Turing-computable.

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Bhupinder Singh Anand. 2003-05-17. Can Turing machines capture everything we can compute?. https://arxiv.org/abs/math/0304379

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