[FOM] inconsistency of P

[Harvey Friedman]

On Oct 1, 2011, at 8:36 AM, Edward Nelson wrote:

...

> The consistency of P remains an open problem.

As I indicated before on the FOM, there is a proof that any given  
finite fragment of PA is consistent, using "every infinite sequence of  
rationals in [0,1] has an infinite Cauchy 1/n subsequence".

Does this at least answer the question of whether PRA or even, say, 3  
quantifier induction, is consistent?

Harvey