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Sniffnoy comments on Harry Potter and the Methods of Rationality discussion thread, part 8 - Less Wrong
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I'd hardly call a well-ordering on one particular cardinality "almost the full strength of AC"! I guess it probably is enough for a lot of practical cases, but there must be ones where one on 2^c is necessary, and even so that's still a long way from the full strength...
I just have a hard time imagining someone who was happy with "c is well-ordered" but for whom "2^c is well-ordered" is a bridge too far.
Hm, agreed. I guess not so much "the full strength" but "the full counterintuitiveness"? Where DC uses hardly any of the counterintuitiveness, and ultrafilter lemma uses nearly all of it?