I'm looking for references for the following facts concerning the ultrafilter lemma (~ "there exist non-principal ultrafilters"):

- The ultrafilter lemma is independent of ZF.
- ZF + the ultrafilter lemma does not imply the Axiom of Choice.

I would prefer an overview article / book that links to the original papers instead of the original papers themselves. That's because I don't rely on these facts; I only want to give some context for my readers.

The Axiom of Choicecovers this material. $\endgroup$ – Ed Dean Mar 22 '11 at 10:18