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.
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.
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.