FOM: Re: your FOM posting on proof theory wtait at
Mon Jul 20 17:23:37 EDT 1998


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.

Incidently, although I received your posting in reply to Neil, I did not 
receive the posting of Neil's from which you quoted. 

Bill Tait

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