 A result of Hausdorff in (1906), that \(\omega_1\), the first uncountable ordinal) is not the limit of a progression of smaller ordinals is shown to follow if one assumes the Axiom of Choice (∗265·49). It is then conjectured that this cannot be shown without relying on the Axiom of Choice. See Grattan-Guinness (2000: 403) for a discussion of Hausdorff’s influence on the content of PM.