FOM: Logic of x >> 0 and x >> y

[Kanovei]

>From: Harvey Friedman <friedman at math.ohio-state.edu>

>
2. Let phi be an arbitrary sentence in the language of PA(St). Can we
figure out whether phi is true? By this I mean, is there always a sentence
psi without S such that PA(St) proves (phi iff psi)? If this fails, is
there an interesting extension of PA(St) so that this holds?
>

I proved near 1991 that this fails for IST but holds for a 
version of IST which considers only those sets which are 
elements of standard sets. 

V.Kanovei