# [FOM] Countable choice

Bill Taylor W.Taylor at math.canterbury.ac.nz
Mon Jun 9 22:41:35 EDT 2008

Thomas Forster:

->I have a feeling that there is a literature on the idea that
->countable choice is not just a weak form of full choice, but
->is somehow a fundamentally different principle: there might
->be good reasons for adopting AC_\omega that aren't special
->cases of arguments for adopting AC.   Can anyone give me
->any pointers to it..?

No pointers, sorry, but whatever philosophical arguments suggest that
AC_w is OK, should certainly apply to DC (dependent choice) as well,
so you might try googling (or otherwise) for that.

It's also intriguing that DC is not just AC for some slightly larger cardinal,
but in fact is a separate sort of principle altogether, (it seems to me);
if you write it down carefully with quantifiers etc, it has quite
a different-looking form.

-- Bill Taylor