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paper-machine comments on Bounded versions of Gödel's and Löb's theorems - Less Wrong
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When I get some time I'll sit down and read these more carefully. However, before that time comes I wanted to congratulate you on tackling these things!
<3
EDIT 1: Remarks on Bounded Goedel's theorem
1) 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?
Other than that, I rewrote the proof as explicitly as I could (supplying some missing details and the like) and found no issues.
Thanks!
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.
I figured as much; after all, in the standard proof one only needs PA around long enough to construct Goedel numbers.