http://www.jazzie.com/ii/math/index.html/
This site provides access to the Axiom of Choice FAQ (Frequently Asked Questions) entitled 'Relevance of the Axiom of Choice'. An up-to-date, complete version of this FAQ is available from the WWW (World WIde Web) location provided above. This FAQ first presents a mathematically equivalent statement which defines the Axiom of Choice (AC). It discusses whether the AC can be derived from the other axioms, whether it is consistent with the other axioms and whether we should, in fact, accept it as an axiom. The FAQ then covers three current theories regarding the AC; the platonism theory, the constructivism theory and finally, the formalism theory. Lastly, the FAQ includes alternatives to the AC and under what conditions the AC is necessary.