From: stre...@mathematik.tu-darmstadt.de
To: "Michael Shulman" <shu...@sandiego.edu>
Cc: "Thomas Streicher" <stre...@mathematik.tu-darmstadt.de>,
"Ambrus Kaposi" <kaposi...@gmail.com>,
"Altenkirch Thorsten" <thorsten....@nottingham.ac.uk>,
"HomotopyT...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] Where is the problem with initiality?
Date: Sat, 26 May 2018 18:47:51 +0200 [thread overview]
Message-ID: <ac2f6239b66c27aa3598ea8d62d10a5f.squirrel@webmail.mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <CAOvivQzH2q8Y=p8pcK4R1sqe1SnCCN=amS=B99dMYZxZy+qL8w@mail.gmail.com>
> Thomas, are you saying that the hard part is proving that the syntax
> of type theory is a CwF? I always thought that was perfectly obvious
> and the hard part was interpreting the syntax into some other CwF.
That was a misunderstanding on my side. Correctness is also quite an issue.
But I thought you just discussed the initiality problem!
For this the laborious part is indeed showing that Lindenbaum-Tarski gives
a model. I mean this is intuitively clear and without any surprises.
If one is not overly formalist one is happy to believe this. I possibly
was more formalist those days (:-
But formulating the correctness in terms of a partial interpretation
function on raw syntax is a nice unorthodox idea. To perform it is also a
bit dull but getting the idea how to proceed took me some time.
If I had thought in terms of initial models for essentially algebraic
theories I wouldn't have proven my completeness theorem but rather relied
on algebraic and variable syntax as obviously “isomorph“.
Thomas
next prev parent reply other threads:[~2018-05-26 16:47 UTC|newest]
Thread overview: 57+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-05-22 5:46 Michael Shulman
2018-05-22 16:47 ` Ambrus Kaposi
2018-05-23 16:26 ` [HoTT] " Thorsten Altenkirch
2018-05-24 5:52 ` Michael Shulman
2018-05-24 8:11 ` Thorsten Altenkirch
2018-05-24 9:53 ` Ambrus Kaposi
2018-05-24 17:26 ` Michael Shulman
2018-05-26 9:21 ` Thomas Streicher
2018-05-26 11:47 ` Michael Shulman
2018-05-26 16:47 ` stre... [this message]
2018-05-27 5:14 ` Bas Spitters
2018-05-28 22:39 ` Michael Shulman
2018-05-29 9:15 ` [HoTT] " Thorsten Altenkirch
2018-05-29 15:15 ` Michael Shulman
2018-05-30 9:33 ` Thomas Streicher
2018-05-30 9:37 ` Thorsten Altenkirch
2018-05-30 10:10 ` Thomas Streicher
2018-05-30 12:08 ` Thorsten Altenkirch
2018-05-30 13:40 ` Thomas Streicher
2018-05-30 14:38 ` Thorsten Altenkirch
2018-05-30 10:53 ` Alexander Kurz
2018-05-30 12:05 ` Thorsten Altenkirch
2018-05-30 19:07 ` Michael Shulman
2018-05-31 10:06 ` Thorsten Altenkirch
2018-05-31 11:05 ` Michael Shulman
2018-05-31 19:02 ` Alexander Kurz
2018-06-01 9:55 ` Martin Escardo
2018-06-01 17:07 ` Martín Hötzel Escardó
2018-06-01 17:43 ` Eric Finster
2018-06-01 19:55 ` Martín Hötzel Escardó
2018-06-01 20:59 ` András Kovács
2018-06-01 21:06 ` Martín Hötzel Escardó
2018-06-01 21:23 ` Michael Shulman
2018-06-01 21:53 ` Eric Finster
2018-06-01 22:09 ` Michael Shulman
2018-06-02 15:06 ` Eric Finster
2018-06-05 20:04 ` Michael Shulman
2018-06-02 5:13 ` Thomas Streicher
2018-06-01 21:52 ` Jasper Hugunin
2018-06-01 22:00 ` Eric Finster
2018-06-01 21:27 ` Matt Oliveri
2018-06-02 5:21 ` Ambrus Kaposi
2018-06-02 6:01 ` Thomas Streicher
2018-06-02 14:35 ` Thorsten Altenkirch
2018-05-30 13:30 ` Jon Sterling
2018-06-05 7:52 ` Andrej Bauer
2018-06-05 8:37 ` David Roberts
2018-06-05 9:46 ` Gabriel Scherer
2018-06-05 22:19 ` Martín Hötzel Escardó
2018-06-05 22:54 ` Martín Hötzel Escardó
2018-06-05 22:12 ` Richard Williamson
2018-06-06 15:05 ` Thorsten Altenkirch
2018-06-06 19:25 ` Richard Williamson
2018-05-29 14:00 ` Jon Sterling
2018-05-30 22:35 ` Michael Shulman
2018-05-31 10:48 ` Martín Hötzel Escardó
2018-05-31 11:09 ` Michael Shulman
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