From: Vladimir Voevodsky <vlad...@ias.edu>
To: Andrew Polonsky <andrew....@gmail.com>
Cc: "Prof. Vladimir Voevodsky" <vlad...@ias.edu>,
Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Different notions of equality; terminology
Date: Mon, 18 Jul 2016 23:05:15 +0200 [thread overview]
Message-ID: <A6563942-EE9F-4CA1-8F68-27DC428824B1@ias.edu> (raw)
In-Reply-To: <b8aa1ee7-80a9-497b-916b-8b31d6eb76b3@googlegroups.com>
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> On Jul 18, 2016, at 10:45 PM, Andrew Polonsky <andrew....@gmail.com> wrote:
>
> Finally, Voevodsky currently distinguishes between "substitutive" and "transportational" equalities. But in his system, both concepts are of the "logical" kind. The effect is therefore to promote "strict" equality to the logical level; so one can reason about it in the object logic, while retaining other properties like the conversion rule.
I am not sure what you mean by this. In fact, I emphasized that the only substitutional equality in MLTTs is the definitional equality that can not be postulated or proved, only checked.
Vladimir.
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next prev parent reply other threads:[~2016-07-18 21:05 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-07-18 20:45 Andrew Polonsky
2016-07-18 21:03 ` [HoTT] " Andrej Bauer
2016-07-18 21:05 ` Vladimir Voevodsky [this message]
2016-07-18 21:13 ` Andrew Polonsky
[not found] ` <2506A3A8-8AC0-4B49-AD1E-D660A7A15245@ias.edu>
[not found] ` <CABcT7WDYqUY=efCTvdRpdW98aDSXpjfHGo9pJz2jBNa3yNXCgQ@mail.gmail.com>
[not found] ` <085E4ACF-BD06-484F-ACA3-17DD6249CF76@ias.edu>
[not found] ` <CABcT7WBKxFhcvuBP66wOcUzU1uPNUqPqXoSYW4aCJv4c8U7iuQ@mail.gmail.com>
2016-07-18 21:45 ` Vladimir Voevodsky
2016-07-18 21:16 ` Dimitris Tsementzis
2016-07-18 21:17 ` Jon Sterling
2016-07-18 21:24 ` Andrew Polonsky
[not found] ` <CAOvivQyZzdyhFFPfqkH4W+Z--78t0LEVWtthLhCpDxUkJNUrMQ@mail.gmail.com>
2016-07-18 22:20 ` Andrew Polonsky
2016-07-18 22:24 ` Jon Sterling
[not found] ` <CAOvivQy44FvN_bVD+nby8t0BnnTYf38dR5=s31_Yv_VsDOzLCA@mail.gmail.com>
2016-07-18 22:43 ` Andrew Polonsky
[not found] ` <CAOvivQw15pOvi9wzWFpB2WcwmgxB=uw-826xNmxUck57VagEQA@mail.gmail.com>
2016-07-18 23:01 ` Andrew Polonsky
2016-07-19 12:53 ` Michael Shulman
2016-07-19 16:49 ` Jon Sterling
2016-07-19 19:07 ` Egbert Rijke
2016-07-20 2:45 ` Dan Licata
2016-07-19 23:19 ` Martin Hotzel Escardo
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