FOM: Re: Reuben Hersh: Mitteilungen der DMV (fwd)

[Vaughan Pratt]

From: peter at galois.geg.mot.com (Peter White)
>If the system operates forever, then it is
>choosing a countably infinite sequence of elements from a
>countably infinite sequence of sets. If the axiom of choice fails
>for countably infinite sequences of sets, then this says that there
>is some fundamental mathematical reason why this system will eventually
>fail.

Luckily for your application, choice is a theorem of Z for any given
finite sequence of nonempty sets.  (But not uniformly: there is no
single such theorem of ZF covering all finite lengths, otherwise one
could prove that the reals can be well-ordered.)

Hence if after making only finitely many choices your system is unable
to make a further choice, it will not be attributable to a failure of
the axiom of choice.

Vaughan Pratt