FOM: Conjecture about true arithmetic

Roger Bishop Jones rbjones at
Thu Oct 15 23:34:49 EDT 1998

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

  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   www:

More information about the FOM mailing list