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arXiv · 0806.4732

On the strength of Hausdorff's gap condition

James Hirschorn
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Abstract

Hausdorff's gap condition was satisfied by his original 1936 construction of an (omega-1,omega-1) 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 (omega-1,omega-1) gap not equivalent to any gap satisfying Hausdorff's condition, from uncountably many random reals.

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James Hirschorn. 2008-06-29. On the strength of Hausdorff's gap condition. https://arxiv.org/abs/0806.4732

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