English

A consistency result on long cardinal sequences

Logic 2019-02-19 v2 General Topology

Abstract

For any regular cardinal κ\kappa and ordinal η<κ++\eta<\kappa^{++} it is consistent that 2κ2^{\kappa} is as large as you wish, and every function f:η[κ,2κ]Cardf:\eta \to [\kappa,2^{\kappa}]\cap Card with f(α)=κf(\alpha)=\kappa for cf(α)<κcf(\alpha)<\kappa is the cardinal sequence of some locally compact scattered space.

Keywords

Cite

@article{arxiv.1901.08921,
  title  = {A consistency result on long cardinal sequences},
  author = {Juan Carlos Martinez and Lajos Soukup},
  journal= {arXiv preprint arXiv:1901.08921},
  year   = {2019}
}

Comments

Minor revision. arXiv admin note: text overlap with arXiv:0712.0584

R2 v1 2026-06-23T07:22:19.817Z