2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158121A celebrated argument of F. Hartogs (1915) deduces the Axiom of Choice from the hypothesis of comparability for any pair of cardinals. We show how each of a sequence of seemingly much weaker hypotheses suffices. Fixing a finite number $k>1$, the Axiom of Choice follows if merely any family of $k$ cardinals contains at least one comparable pair.8 pages with an appendix by Andreas BlassLogic03E25text