We give an equivalent, but simpler formulation of the axiom SEP, which was introduced in [9] in order to capture some of the combinatorial behaviour of models of set theory obtained by adding Cohen reals to a model of CH. Our formulation shows that many of the consequences of the weak Freese-Nation property of 𝒫(ω) studied in [6] already follow from SEP. We show that it is consistent that SEP holds while 𝒫(ω) fails to have the (ℵ₁,ℵ ₀)-ideal property introduced in [2]. 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, answering a question of Blass.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-3,
author = {Saka\'e Fuchino and Stefan Geschke},
title = {Some combinatorial principles defined in terms of elementary submodels},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {233-255},
zbl = {1051.03035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-3}
}
Sakaé Fuchino; Stefan Geschke. Some combinatorial principles defined in terms of elementary submodels. Fundamenta Mathematicae, Tome 184 (2004) pp. 233-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-3/