English

Remarks on a paper by Juh\'asz and Kunen

Logic 2007-05-23 v1

Abstract

We give an equivalent, but simpler formulation of the axiom SEP introduced by Juhasz and Kunen. Our formulation shows that many of the consequences of the weak Freese-Nation Property of P(ω)\mathcal P(\omega) already follow from SEP. We show that it is consistent that SEP holds while P(ω)\mathcal P(\omega) fails to have the (1,0)(\aleph_1,\aleph_0)-ideal property, which has been introduced by Hart and Dow . This answers a question addressed independently by Fuchino and by Kunen. We also consider some natural variants of SEP and show that certain changes in the definition of SEP do not lead to a different principle. This answers a question addressed by Blass.

Keywords

Cite

@article{arxiv.math/0309297,
  title  = {Remarks on a paper by Juh\'asz and Kunen},
  author = {Sakae Fuchino and Stefan Geschke},
  journal= {arXiv preprint arXiv:math/0309297},
  year   = {2007}
}