From: Matt Oliveri <atm...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] A small observation on cumulativity and the failure of initiality
Date: Mon, 16 Oct 2017 09:34:10 -0700 (PDT) [thread overview]
Message-ID: <527dc7a5-b3c2-44e2-9d3b-2d47dc118fcf@googlegroups.com> (raw)
In-Reply-To: <CAOvivQzmwxSkdev2FT5WM3A6uanGRg9isGrpF-HWd5DUfwK9cQ@mail.gmail.com>
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On Monday, October 16, 2017 at 11:01:13 AM UTC-4, Michael Shulman wrote:
>
> On Mon, Oct 16, 2017 at 5:30 AM, Neel Krishnaswami
> <neelaka...@gmail.com <javascript:>> wrote:
> > 1. The addition of universes is an open problem. Basically the logical
> > strength of the theory goes up and the proof of Harper and Pfenning
> > needs to be redone. (They exploited the fact that LF doesn't have
> > large eliminations to do a recursion on the size of the type.)
> >
> > I would be rather surprised if this couldn't be made to work, though.
>
> Me too.
>
I was thinking that where you'd really get in trouble is with impredicative
quantifiers. From what I understand, hereditary substitutions are a variant
of cut elimination, which can't directly handle impredicativity. But so
far, HoTT has added impredicativity with an axiom, so maybe it'll work out
somehow. Like HoTT's proof-theoretic strength would be impredicative, but
its "coherence strength" would still be predicative in some weird sense.
That would be a bit unnatural though, in my opinion.
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next prev parent reply other threads:[~2017-10-16 16:34 UTC|newest]
Thread overview: 47+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-10-12 18:43 Dimitris Tsementzis
2017-10-12 22:31 ` [HoTT] " Michael Shulman
2017-10-13 4:30 ` Dimitris Tsementzis
2017-10-13 15:41 ` Michael Shulman
2017-10-13 21:51 ` Dimitris Tsementzis
2017-10-13 0:09 ` Steve Awodey
2017-10-13 0:44 ` Alexander Altman
2017-10-13 15:50 ` Michael Shulman
2017-10-13 16:17 ` Steve Awodey
2017-10-13 16:23 ` Michael Shulman
2017-10-13 16:36 ` Matt Oliveri
2017-10-14 14:56 ` Gabriel Scherer
2017-10-15 7:45 ` Thomas Streicher
2017-10-15 8:37 ` Thierry Coquand
2017-10-15 9:26 ` Thomas Streicher
2017-10-16 5:30 ` Andrew Polonsky
2017-10-15 10:12 ` Michael Shulman
2017-10-15 13:57 ` Thomas Streicher
2017-10-15 14:53 ` Michael Shulman
2017-10-15 16:00 ` Michael Shulman
2017-10-15 21:00 ` Matt Oliveri
2017-10-16 5:09 ` Michael Shulman
2017-10-16 12:30 ` Neel Krishnaswami
2017-10-16 13:35 ` Matt Oliveri
2017-10-16 15:00 ` Michael Shulman
2017-10-16 16:34 ` Matt Oliveri [this message]
2017-10-16 13:45 ` Matt Oliveri
2017-10-16 15:05 ` Michael Shulman
2017-10-16 16:20 ` Matt Oliveri
2017-10-16 16:37 ` Michael Shulman
2017-10-16 10:01 ` Thomas Streicher
2017-10-15 20:06 ` Matt Oliveri
2017-10-13 8:03 ` Peter LeFanu Lumsdaine
2017-10-13 8:10 ` Thomas Streicher
2017-10-14 7:33 ` Thorsten Altenkirch
2017-10-14 9:37 ` Andrej Bauer
2017-10-14 9:52 ` Thomas Streicher
2017-10-14 10:51 ` SV: " Erik Palmgren
2017-10-15 23:42 ` Andrej Bauer
2017-10-15 10:42 ` Thorsten Altenkirch
2017-10-13 22:05 ` Dimitris Tsementzis
2017-10-13 14:12 ` Robin Adams
[not found] <B14E498C-FA19-41D2-B196-42FAF85F8CD8@princeton.edu>
2017-10-14 9:55 ` [HoTT] " Alexander Altman
2017-10-16 10:21 Thorsten Altenkirch
2017-10-16 10:42 ` Andrew Polonsky
2017-10-16 14:12 ` Thorsten Altenkirch
2017-10-16 10:21 Thorsten Altenkirch
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