FOM: Conjecture about true arithmetic

[Roger Bishop Jones]

In the course of considering a recent philosophical paper on 
the "determinateness" of arithmetic I came up with the following
conjecture:

  The first order theory whose non-logical axioms are:
    1. The peano axioms
    2. The negation of every closed sentence of first order
       arithmetic which is w-inconsistent with PA
  is "true arithmetic" (the sentences of arithmetic which are true
  in the standard model).

Can anyone tell me whether this is a known result, (or an obvious
corollary of one, or obviously refuted by one) and if so where
the result is proved?

Roger Jones

email: rbjones at rbjones.com   www:  http://www.rbjones.com/