[FOM] Question on Incompleteness Theorems

[Dmytro Taranovsky]

Is there an arithmetical formula phi with one free variable such that
for every Pi-0-1 formula psi with one free variable it is consistent
with Peano Arithmetic that 
Forall n (phi(n) <--> psi(n)).
Can phi be a Pi-0-1 formula?

My motivation for this question is (in part) finding the strongest
possible forms of the incompleteness results.

Dmytro Taranovsky