On the strength of Hausdorff's gap condition

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

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Logic, 03E05 (Primary); 03E40, 28E15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/163857

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.4732
 http://arxiv.org/abs/0806.4732

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arXiv