Remarks on a paper by Juhász and Kunen

Sakae Fuchino; Stefan Geschke

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Remarks on a paper by Juhász and Kunen

Sakae Fuchino·Stefan Geschke

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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 $\mathcal P(ω)$ already follow from SEP. We show that it is consistent that SEP holds while $\mathcal P(ω)$ fails to have the $(\aleph_1,\aleph_0)$-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.

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BibTeX RIS

Sakae Fuchino, Stefan Geschke. 2003-09-18. Remarks on a paper by Juhász and Kunen. https://arxiv.org/abs/math/0309297

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