On the strength of Hausdorff's gap condition

2008/06/29 by James Hirschorn, Hirschorn, James
Computer Science · Mathematics · #03E05 (Primary) #03E40 #28E15 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E05 #msc:03E40 #msc:28E15

paper · pdf · doi:10.48550/arxiv.0806.4732

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

arxiv created 2008/06/29 · openalex publication_date 2008/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Sur les caractères de convergence des séries a termes positifs et sur les fonctions indéfiniment croissantes

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