Arithmetisation dans le topos

Arithmetisation dans le topos

[David Roberts]

Dear all,

some years back I put out a call for any information about Joyal's
lecture(s) containing his arithmetic universe proof of Gödel's
incompleteness theorem. It was suggested I ask Anders Kock, and he was
able to give me if not that lecture, but a related lecture from 1974,
with the above title. It contained a rough definition of an arithmetic
universe, namely a pretopos in which the free category on any internal
graph exists. There was also some good material on classifying
toposes.

For historical interest I have made the notes available, with Anders'
permission, here:

https://thehighergeometer.wordpress.com/2019/05/08/joyal-arithmetisation-dans-le-topos/

Others may be interested as to the state of the art at the time.

I hope that one day we will see details of the incompleteness proof
that still eludes my grasp!

Best regards,
David

David Roberts
Webpage: https://ncatlab.org/nlab/show/David+Roberts
Blog: https://thehighergeometer.wordpress.com


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