English

On the strength of Hausdorff's gap condition

Logic 2008-07-01 v1

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.

Cite

@article{arxiv.0806.4732,
  title  = {On the strength of Hausdorff's gap condition},
  author = {James Hirschorn},
  journal= {arXiv preprint arXiv:0806.4732},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T10:55:30.028Z