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If the UTM Theorem states there's a u such that u(e,x) = f(x) where both
are defined and both are undefined when either is undefined, is that
interesting or surprising to anybody?
The identity function is valid for u and forces that e = f. Job done.
Am I missing something? Isn't it just trivially deducible from the
identity introduction axiom when you have it, which we assume when we
haven't fully formalised our discussion of computation.
--
Tristan Wibberley
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| Date | Sujet | # | Auteur | |
| 21 Oct 25 |  UTM Theorem vs the identity function | 12 | Tristan Wibberley | |
| 21 Oct 25 |  Re: UTM Theorem vs the identity function | 8 | Pierre Asselin | |
| 22 Oct 25 |   Re: UTM Theorem vs the identity function | 7 | Tristan Wibberley | |
| 22 Oct 25 |  Re: UTM Theorem vs the identity function | 3 | olcott | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 22 Oct 25 |  Re: UTM Theorem vs the identity function --- Gödel | 1 | olcott | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 3 | Pierre Asselin | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 1 | Pierre Asselin | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 3 | Mikko | |
| 22 Oct 25 | Re: UTM Theorem vs the identity function | 2 | Tristan Wibberley | |
| 23 Oct 25 | Re: UTM Theorem vs the identity function | 1 | Mikko |
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