Re: Jech's proof of Gödel's second incompleteness theorem

[Joseph Helfer]

Thank you, Vaughan.
I found there is also a published version, which is, helpfully, a little less terse:
https://www.ams.org/journals/proc/1994-121-01/S0002-9939-1994-1191869-1/S0002-9939-1994-1191869-1.pdf

It is an interesting note. It seems to suggest a similar, simpler proof:
Suppose Σ is consistent and proves that a model of Σ exists.
Following Jech, we then see that for any model M of Σ, there must be N∈M which is also a model.
But now, we know that we can take M to be a *well-founded* model (say, a transitive model).
However, repeating the above argument, we get a sequence of models M1∋M2∋M3∋⋯
A contradiction.
??

Best,
Joj

________________________________
From: FOM <fom-bounces at cs.nyu.edu> on behalf of Vaughan Pratt <pratt at cs.stanford.edu>
Sent: Sunday, September 11, 2022 9:54 AM
To: fom at cs.nyu.edu <fom at cs.nyu.edu>
Subject: Jech's proof of Gödel's second incompleteness theorem


In response to Adriano Palma's request, Thomas Jech submitted his proof of Gödel's second incompleteness theorem to arXiv on April 15, 1992.  It can be downloaded from https://arxiv.org/abs/math/9204207<https://urldefense.com/v3/__https://arxiv.org/abs/math/9204207__;!!LIr3w8kk_Xxm!qvtXaxJZ_cczsYkFubJWHv_56A7QplhZTRCJ_49YcyuR2IqqDqTnpuaztYmDCfoqpRH1B7W6n9DjsFb73Bs$> .  Hopefully that's what Adriano wanted.

Vaughan Pratt
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