[FOM] Question on Incompleteness Theorems

Tue Jun 1 13:38:59 EDT 2004

On May 31, 2004, at 02:20, Dmytro Taranovsky wrote:

> 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?

Apart from Mitchell Spector's reply, a positive solution can be found in

S.A.Kripke. "Flexible" predicates of formal number theory. Proc.AMS 
13(1962)647-650.

regards,
Volodya Shavrukov