English

Successive failures of approachability

Logic 2018-06-12 v2

Abstract

Motivated by showing that in ZFC we cannot construct a special Aronszajn tree on some cardinal greater than 1\aleph_1, we produce a model in which the approachability property fails (hence there are no special Aronszajn trees) at all regular cardinals in the interval [2,ω2+3][\aleph_2, \aleph_{\omega^2+3}] and ω2\aleph_{\omega^2} is strong limit.

Cite

@article{arxiv.1702.05062,
  title  = {Successive failures of approachability},
  author = {Spencer Unger},
  journal= {arXiv preprint arXiv:1702.05062},
  year   = {2018}
}
R2 v1 2026-06-22T18:20:28.098Z