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

Joseph Helfer jhelfer at
Mon Sep 12 17:47:05 EDT 2022

Thank you, Vaughan.
I found there is also a published version, which is, helpfully, a little less terse:

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.


From: FOM <fom-bounces at> on behalf of Vaughan Pratt <pratt at>
Sent: Sunday, September 11, 2022 9:54 AM
To: fom at <fom at>
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<;!!LIr3w8kk_Xxm!qvtXaxJZ_cczsYkFubJWHv_56A7QplhZTRCJ_49YcyuR2IqqDqTnpuaztYmDCfoqpRH1B7W6n9DjsFb73Bs$> .  Hopefully that's what Adriano wanted.

Vaughan Pratt
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