On the Strength of Hausdorff’s Gap Condition


Abstract. Hausdorff’s gap condition was satisfied by his original 1936 construction of an (ω1, ω1) gap in P(N) / Fin. We solve an open problem in determining whether Hausdorff’s condition is actually stronger than the more modern indestructibility condition, by constructing an indestructible (ω1, ω1) gap not equivalent to any gap satisfying Hausdorff’s… (More)


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