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Abstract: A celebrated argument of F. Hartogs 1915 deduces the Axiom of Choice fromthe hypothesis of comparability for any pair of cardinals. We show how each ofa sequence of seemingly much weaker hypotheses suffices. Fixing a finite number$k>1$, the Axiom of Choice follows if merely any family of $k$ cardinalscontains at least one comparable pair.



Author: David Feldman, Mehmet Orhon, Andreas Blass

Source: https://arxiv.org/







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