cousin_it comments on Bounded versions of Gödel's and Löb's theorems - Less Wrong

32 Post author: cousin_it 27 June 2012 06:28PM

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Comment author: cousin_it 28 June 2012 07:07:58AM *  2 points [-]

Thanks!

It is unclear (to me, who has not studied such things in several years) where the proof uses the fact that T includes PA. Maybe it is necessary for the construction of R?

Saying that T includes PA is shorthand for the usual Gödelian requirement that T includes the basic arithmetical truths necessary to formalize the bits of common-sense reasoning used in the proof, like simulating the execution of R.

Comment author: [deleted] 28 June 2012 08:11:20AM 2 points [-]

I figured as much; after all, in the standard proof one only needs PA around long enough to construct Goedel numbers.