Nelson's proof of the inconsistency of arithmetic What are the prerequisites to understand Nelson's attempted proof of the inconsistency of arithmetic and the subsequent "famous" discussion on John Baez's blog? I have a reasonable background in mathematical logic (beginning graduate level), but Nelson's outline contains a lot of material/terminology that I'm not familiar with, such as: Hilbert-Ackermann consistency theorem, open theories, relativization schemata, and the BCL theorem. I want to know if it is feasible to learn this background material in (say) 2-3 weeks of study and where I can best start. I think the Nelson "incident" is a fascinating note in modern mathematical history, but there is a lot of other cool stuff out there and I don't want to invest too much time in learning material that will only benefit me in understanding Nelson's "proof" (or are these concepts of more general interest as well?).
I understand this question is somewhat hard to answer precisely, but that is not the point. If someone can put me in the right direction/ballpark I would already be very happy.
 A: I agree with you that Nelson's "proof" is very interesting! Indeed, as remarked in this article (which I linked in another of your questions), we are not alone in this assessment: " Some very nice and unexpected mathematics ensued in the shadow of Nelson’s interpretability program (and related
studies), not only by Nelson himself but also by Robert Solovay, Petr Hajek,
Samuel Buss, Alex Wilkie, Jeff Paris, Pavel Pudlak, Albert Visser and others." (p. 2) If Solovay found it interesting, I think we are in good company.
As for background, it seems clear to me that the first four chapters of Shoenfield, which are also frequently referred to by Nelson, are a good start. In particular, the Hilbert-Ackermann consistency theorem is proved on p. 49ff, open theories are defined on p. 48, etc. Nelson's Predicative Arithmetic also contains much of the background needed (e.g. he defines a relativization of a formula on p. 5; the schemata of Solovay are probably the ones mentioned on p. 12). Chaitin's theorem is sketched in Boolos, Jeffrey & Burgess's Computability and Logic (5ed), chapter 17. As for BLC, I know next to nothing about complexity theory, so I can't be much of help here.
Also, the freely available Hájek and Pudlák also contains most of the needed background, including a crash course on complexity theory (with a definition of polynomial time, etc.). So you may want to study that too.
