I have read up, in Shoenfield and elsewhere, on a lot of the details involved in Nelson's failed proof of the inconsistency of arithmetic. I understand the Kritchman-Raz proof; the proof of the Hilbert-Ackermann consistency theorem; what the rank and level of a special constant are; what a $(\rho, \lambda)$-proof of $A$ in $T$ is, and why there always exist such $(\rho, \lambda)$ for any closed $A$. But I still cannot make any sense of Nelson's argument below (I'm trying to understand why it fails). Can someone explain what he is doing? I would like to be more specific, but I don't understand this part of Nelson's outline from the very beginning (already concerning "the proofs $\pi$ of (9)").
Btw, I don't know exactly what $Q_0^*$ is (other than some stronger version of $Q_0$), but I believe that's not such an important issue in order to understand Nelson's idea. I'm willing to take it on faith what Nelson claims concerning $Q_0^*$.
