Re: Absolute Continuity

<snip>

Since computer scientists (computer scientists, not
physicists or
mathematicians) are not willing to part with
recursion (just go and ask
them), maybe mr. de Bruijn can give us a
computational model without using
infinite sets and yet sufficiently strong to do
recursion. Should be
funny, considering that the recursion theorem and
the axiom of infinity
are essentially equivalent...

Really? No.


No, what? That the axiom of infinity is essentially equivalent to the recursion theorem is well known to topos theorists. There are some subtleties here, which is why I wrote "essentially" (e.g. not all definitions of infinite object are equivalent) but if it gives you any consolation, the argument is constructively valid.

Regards,
G. Rodrigues
.

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