# FOM: Re: your FOM posting on proof theory

wtait@ix.netcom.com wtait at ix.netcom.com
Mon Jul 20 17:23:37 EDT 1998

Jeremy,

I have been enjoying your discussion of proof theory. But a small remark

>The idea is this: the stronger a theory is, the more recursive ordinals it
>"knows about," i.e. the more powerful the transfinite induction
>principles it can derive. So determining this ordinal measures, in a
>sense, the strength of the theory.

That is the idea; but of course, as you know, the proof theoretic ordinal
is too crude a measure. T+Consis_T---or, indeed, T+\phi, where \phi is
any true sigma^1_1 sentence---will have the same proof theoretic ordinal
as T.