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MoeBlee wrote:
> Bill Taylor wrote:
> > They insist on keeping a fuzzy view on what is the largest
> > feasible number
>
> Thank you for your post and all the questions in it. I hope it gets a
> lot of response.
>
> A related question that I have, which you or perphas others can help
> with, is that of the putative axiomatizations of utltrafinitist
> mathematics.
Yessenin-Volpin said explicitly that he didn't want to commit to a
specific axiomatic theory. Edward Nelson, on the other hand, has done
some interesting research about certain weak axiomatic theories in
arithmetic, which may embody his stance. See his book "Predicative
Arithmetic". Edward Nelson has put active effort into proving certain
results in these weak arithmetics. Success would imply that Peano
Arithmetic is inconsistent.
> Do these axiomatizations really hold up as formal
> (recursively axiomatized) systems? Do they really provide systems such
> that there is an effective method to check whether a string of formulas
> is a proof and still have only finitely many natural numbers and still
> also allow for proofs of theorems that serve to provide the basic
> mathematics (or some version of) calculus?
>
> MoeBlee
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