From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Andrej Bauer <andrej...@andrej.com>
Cc: Martin Escardo <escardo...@googlemail.com>,
"HomotopyT...@googlegroups.com" <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Meta-conjecture about MLTT
Date: Mon, 12 Sep 2016 13:14:21 +0200 [thread overview]
Message-ID: <20160912111420.GA14499@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <CAB0nkh2eZT+yOVDmdxPdkg2iKuvJFU2W=Qd_MmM1=CW9tFrDNw@mail.gmail.com>
I am afraid this skeleton model is not split and spliiting it it wan't
be a skeleton anymore.
Thomas
On Mon, Sep 12, 2016 at 01:02:24PM +0200, Andrej Bauer wrote:
> Let me try.
>
> Consider the model of MLTT in the skeleton of sets, i.e., types are
> interpreted as cardinal numbers and functions are the set-theoretic
> functions between cardinals. The identity type is just what you'd
> expect in a set-theoretic model (in fact, there is *no* choice about
> i). There are no problems of coherence anywhere.
>
> This model validates equality reflection. If MLTT+reflection
> distinguished isomorphic types, then there would exist in this model
> two isomorphic types which are not equal, but since we started with a
> skeleton this will not do.
>
> It is a bit amusing that the model also validates things like Id(U,
> Nat -> Nat, Nat -> Bool) and is thus quite educational.
>
> It is a model, right?
>
> With kind regards,
>
> Andrej
>
next prev parent reply other threads:[~2016-09-12 11:14 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 [this message]
2016-09-12 11:23 ` Andrew Polonsky
2016-09-12 11:41 ` Thomas Streicher
2016-09-12 12:47 ` Thomas Streicher
2016-09-12 13:01 ` Martin Escardo
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