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Rupert wrote:
> He announced that he had a
> consistency proof for ZF with any finite number of inaccessible
> cardinals
I don't understand that. If he's an ultrafinitist, then how could he
use inaccessible cardinals? Or, is he claiming to prove the
inconsistency of ZF by proving that ZF + "inaccessible cardinals exist"
(which is relatively consistent to ZF?) proves the consistency of ZF?
> http://math.ucsd.edu/~sbuss/ResearchWeb/nelson/paper.pdf
Thanks, that one is free and it looks like good reading.
> I don't think they would go about it that way. They could use a very
> weak arithmetic in which only functions of very low computational
> complexity could be proved total. Then only fairly small numbers could
> be feasibly defined. They could even add an axiom saying that e.g. the
> exponential function is not total, which would give rise to a theory
> with nonstandard models. Nelson developed an alternative foundation for
> probability theory using such an arithmetic.
Hmm, I think I get the gist of that. Eventually, I'll look into it.
MoeBlee
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