# [FOM] Interpretability in Q

Daniel Mehkeri dmehkeri at gmail.com
Wed Oct 12 21:11:05 EDT 2011

Richard Heck writes:
> As I understand him, Nelson is prepared to accept (i) Q and (ii) as
> much induction as is interpretable in Q

Later:

> In particular, I\Delta_0 + \omega_1 proves that it can itself be
> interpreted in Q

But then, that can't be a reason for accepting I\Delta_0 + \Omega_1.

Is there something weaker than I\Delta_0 + \Omega_1 that proves
I\Delta_0 + \Omega_1 to be interpretable in Q? (And what proves _that_
to be interpretable in Q, and so on?)

I scanned _Predicative Arithmetic_ and didn't see this answered. The
meta-theorems do seem to require some meta-theory like the one
mentioned, which, for finitary reasons, we know to be interpretable in
Q. But what is Nelson's reason for accepting it?

Daniel Mehkeri



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