From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Martin Escardo <escardo...@googlemail.com>
Cc: "HomotopyT...@googlegroups.com" <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Meta-conjecture about MLTT
Date: Mon, 12 Sep 2016 14:47:47 +0200 [thread overview]
Message-ID: <20160912124747.GC15456@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <5fb00299-f5c6-c63c-aade-a688ba2e5f4b@googlemail.com>
> The meta-task is to either produce two isomorphic types in an empty context,
> together with a property that one of them provably has but the other
> doesn't, or to show that this is impossible.
This seems to be hard but in my eyes is not the right question. What
Andrew has shown is that there are definable isomorphic types A and B
in a universe U and a predicate P on this universe where P(A) is
inhabited but P(B)° isnot. Actually, this argument is generic since
one may take P(X) = IdU;A,X).
It's like in programming language semantics. One thing is to
distinguish by maps to 2 and another is to distinguis by maps to \Sigma.
Inhabited plays the role of \top and not inhabited plays the role of \bot.
Thomas
next prev parent reply other threads:[~2016-09-12 12:47 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-11 20:47 Martin Escardo
2016-09-11 22:08 ` [HoTT] " Peter LeFanu Lumsdaine
2016-09-11 22:26 ` Martin Escardo
2016-09-12 9:11 ` Thomas Streicher
2016-09-12 5:20 ` Andrew Polonsky
2016-09-12 5:59 ` [HoTT] " Jason Gross
2016-09-12 9:55 ` Andrew Polonsky
2016-09-12 10:07 ` Andrew Polonsky
2016-09-12 10:35 ` Nicolai Kraus
2016-09-12 10:16 ` Peter LeFanu Lumsdaine
2016-09-12 10:44 ` [HoTT] " Nicolai Kraus
2016-09-12 11:02 ` Andrej Bauer
2016-09-12 11:14 ` Thomas Streicher
2016-09-12 11:23 ` Andrew Polonsky
2016-09-12 11:41 ` Thomas Streicher
2016-09-12 12:47 ` Thomas Streicher [this message]
2016-09-12 13:01 ` Martin Escardo
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