Re: [HoTT] Voevodsky obituary in Nature

["Martín Hötzel Escardó" <"escardo..."@gmail.com>]

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On Tuesday, 7 November 2017 21:50:24 UTC, Dimitris Tsementzis wrote:
>
> Dan,
>
> It is an interesting idea to refer to univalence as a “mechanism” rather 
> than an “axiom”.
>
> Even if you did it for expository reasons, I believe that in certain 
> contexts it is a good phrase to adopt.
>

I very much like this way of expression, too, even though univalence became 
a mechanism for the first time with cubicaltt.

Nevertheless, although Vladimir certainly didn't have a mechanism for 
univalence, he envisioned its possibility, and even formulated a conjecture 
that is still unsettled, namely that if univalence implies that there is a 
*number* n:N with a property P(n), then we can find, metatheoretically, 
using an algorithm, a *numeral* n':N (a closed term of type N) and a proof 
that univalence implies P(n'). No mechanism for univalence can currently 
provide that, as far as I know.

Martin 
 

>
> Dimitris
>
> On Nov 7, 2017, at 16:40, Daniel R. Grayson <daniel...@gmail.com 
> <javascript:>> wrote:
>
> See https://www.nature.com/articles/d41586-017-05477-9
>
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