On the strength of Hausdorff's gap condition

Details On the strength of Hausdorff's gap condition On the strength of Hausdorff's gap condition

2008-06-29

arxiv.org/abs/0806.4732v1

Mathematics

Logic

9 pages. Original 2002 version. Article homepage: http://homepage.univie.ac.at/James.Hirschorn/research/Hausdorff.gap/Hausdorf

Scientific paper

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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