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Eugine_Nier comments on Harry Potter and the Methods of Rationality discussion thread, part 8 - Less Wrong
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This isn't quite right. The consistency of ZF + DC + "every subset of R is Lebesgue measurable" is equivalent to the consistency of an inaccessible cardinal, which is a much stronger assumption then the consistency of ZFC + Con(ZFC).
Sorry, my mistake. Still, set theorists usually believe this.