From: "Joyal, André" <"joyal..."@uqam.ca>
To: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
Cc: Ulrik Buchholtz <ulrikbu...@gmail.com>,
Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: RE: [HoTT] Identity versus equality
Date: Mon, 11 May 2020 14:54:25 +0000 [thread overview]
Message-ID: <8C57894C7413F04A98DDF5629FEC90B1652F5861@Pli.gst.uqam.ca> (raw)
In-Reply-To: <20200511073332.GA30513@mathematik.tu-darmstadt.de>
Thank you for pointing out the case of the universe of constructible sets L.
It is internal to ZF because it is was constructed from ordinals in ZF.
Could it be also external to ZF ?
Gödel thought that ordinals and sets are real, like matter, but of a different kind.
He was the first to use the full power of mathematics for studying formal logic.
Most logicians believe that natural numbers are real.
They use natural numbers and induction for studying formal systems.
Best,
André
PS: It is not easy to stop participating to this interesting discussion!
________________________________________
From: Thomas Streicher [stre...@mathematik.tu-darmstadt.de]
Sent: Monday, May 11, 2020 3:33 AM
To: Joyal, André
Cc: Ulrik Buchholtz; Homotopy Type Theory
Subject: Re: [HoTT] Identity versus equality
Dear Andr"e,
the exo/endo distinction is different from external/internal. It is like
L in set theory ZF which does not allow one to prove consisteny of ZF.
(An aside: why do internal cats play such an important role in traditional
topos theory and are evil in Hott?)
Thomas
next prev parent reply other threads:[~2020-05-11 14:54 UTC|newest]
Thread overview: 61+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-05-05 8:47 Ansten Mørch Klev
2020-05-06 16:02 ` [HoTT] " Joyal, André
2020-05-06 19:01 ` Steve Awodey
2020-05-06 19:18 ` Michael Shulman
2020-05-06 19:31 ` Steve Awodey
2020-05-06 20:30 ` Joyal, André
2020-05-06 22:52 ` Thorsten Altenkirch
2020-05-06 22:54 ` Thorsten Altenkirch
2020-05-06 23:29 ` Joyal, André
2020-05-07 6:11 ` Egbert Rijke
2020-05-07 6:58 ` Thorsten Altenkirch
2020-05-07 9:04 ` Ansten Mørch Klev
2020-05-07 10:09 ` Thomas Streicher
2020-05-07 16:13 ` Joyal, André
2020-05-07 21:41 ` David Roberts
2020-05-07 23:43 ` Joyal, André
2020-05-07 23:56 ` David Roberts
2020-05-08 6:40 ` Thomas Streicher
2020-05-08 21:06 ` Joyal, André
2020-05-08 23:44 ` Steve Awodey
2020-05-09 2:46 ` Joyal, André
2020-05-09 3:09 ` Jon Sterling
[not found] ` <CADZEZBY+3z6nrRwsx9p-HqYuTxAnwMUHv7JasHy8aoy1oaGPcw@mail.gmail.com>
2020-05-09 2:50 ` Steve Awodey
2020-05-09 8:28 ` Thomas Streicher
2020-05-09 15:53 ` Joyal, André
2020-05-09 18:43 ` Thomas Streicher
2020-05-09 20:18 ` Joyal, André
2020-05-09 21:27 ` Jon Sterling
2020-05-10 2:19 ` Joyal, André
2020-05-10 3:04 ` Jon Sterling
2020-05-10 9:09 ` Thomas Streicher
2020-05-10 11:59 ` Thorsten Altenkirch
2020-05-10 11:46 ` Thorsten Altenkirch
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:20 ` Nicolai Kraus
2020-05-10 14:34 ` Michael Shulman
2020-05-10 14:52 ` Nicolai Kraus
2020-05-10 15:16 ` Michael Shulman
2020-05-10 15:23 ` Nicolai Kraus
2020-05-10 16:13 ` Nicolai Kraus
2020-05-10 16:28 ` Michael Shulman
2020-05-10 18:18 ` Nicolai Kraus
2020-05-10 19:15 ` Thorsten Altenkirch
2020-05-10 19:20 ` Thorsten Altenkirch
2020-05-10 12:53 ` Ulrik Buchholtz
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:27 ` Nicolai Kraus
2020-05-10 15:35 ` Ulrik Buchholtz
2020-05-10 16:30 ` Michael Shulman
2020-05-10 18:56 ` Nicolai Kraus
2020-05-10 18:04 ` Joyal, André
2020-05-11 7:33 ` Thomas Streicher
2020-05-11 14:54 ` Joyal, André [this message]
2020-05-11 16:37 ` stre...
2020-05-11 16:42 ` Michael Shulman
2020-05-11 17:27 ` Thomas Streicher
2020-05-10 16:51 ` Nicolai Kraus
2020-05-10 18:57 ` Michael Shulman
2020-05-10 19:18 ` Nicolai Kraus
2020-05-10 20:22 ` Michael Shulman
2020-05-10 22:08 ` Joyal, André
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