[FOM] Godel Sentence

[Richard Heck]

>In fact, also a Godel-sentence G is only *equivalent* to a sentence
>"expressing the unprovability of G" - at least in all books I have seen
>the claim is that G<-> -Pr_T([G]) is a theorem of T, not that G is *identical*
>to -Pr_T([G]) (which clearly cannot be the case). 
>
This is a bit off-thread, but I worried a good deal about this issue a 
little while ago, and even posted a few messages about the problem here. 
(I believe Torkel may have commented on those posts, as well.) There are 
a number of subtleties here. But this last assertion is true only for 
certain familiar sorts of Goedel numberings. It is possible to massage 
the coding so that G *is* identical to ~Pr_T([G]). I expect, in fact 
(though I have not proved), that it is possible to do this uniformly, so 
that for every formula A(x) there is a sentence G_A such that G_A is the 
sentence A([G_A]).

Richard