This site has a number of good links on AC.
I have had a tough time understanding the reasoning of axiomatic set theory. I suspect that one of the reasons is that in my mind ALL is equated with EVERY, and that for infinite elements that is inappropriate.
IN particular, I have a tough time figuring how the Axiom of choice is independent of the axiom of subsets, sum Set, and of replacement.
Anybody can point me to an author / resource that takes the time to go over the delicacies of working with infinite arguments?
One of the tenets of intuitionism is rejection of -- I forgot the terms -- actual (?) infinity and accepting infinity only in the sense that one can generate any finite number of elements. You can read about this in Wikipedia or Standford Encyclopedia of Philosophy.