# [FOM] Consistency of P

Richard Heck rgheck at brown.edu
Tue Oct 4 11:25:46 EDT 2011

Arnon Avron wrote:
> Can Nelson understand what is Pi^0_0 statement? How?
> Can he understand what is a formula? How?
> Can he understand what is a proof? How?
>
As I understand him, Nelson is prepared to accept (i) Q and (ii) as
much induction as is interpretable in Q. If so, however, then he has
no problem understanding such notions. In particular, the theory
I\Delta_0 + \omega_1 is interpretable in Q, and all of these notions
can be defined there and their basic properties proven.

Indeed, Visser once remarked that I\Delta_0 + \omega_1 is "just
right" for syntax. That is why it has played such a significant role in
the study of interpretability.

Richard Heck

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Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University