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Eric Boniface (Jul 19 2024 at 18:33):I found this discussion from 2019 by Michael Weiss and John Baez on trying to formulate Godel's completeness theorem in the language of Boolean hyperdoctrines. https://diagonalargument.com/mathnotes/first-order-categorical-logic-the-series/
Unfortunately, it ends on a cliffhanger and stops after defining a notion of an inconsistent hyperdoctrine. Has there been any further work on trying to formulate a completeness theorem for Boolean hyperdoctrines? Furthermore, has there been any work on trying to formulate the standard theorems of classical model theory in a similar way, such as the Lowenheim-Skolem theorem or compactness?
John Baez (Jul 19 2024 at 20:17):Not by us, alas. A lot of this would be quite easy for a real expert, I imagine. But I'd been wanting to work it out for myself.
Julius Hamilton (Jul 27 2024 at 03:56):I’d like to discuss this to learn more about how it might work.
John Baez (Jul 27 2024 at 11:05):If I had the energy to talk about it, I'd use that energy to keep working on this with Michael Weiss. I'm thinking about other things now.