Re: Jech's proof of Gödel's second incompleteness theorem
Joseph Helfer
jhelfer at usc.edu
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:
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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