Some combinatorial principles defined in terms of elementary submodels

Sakaé Fuchino, and Stefan Geschke. "Some combinatorial principles defined in terms of elementary submodels." Fundamenta Mathematicae 181.3 (2004): 233-255. <http://eudml.org/doc/283366>.

@article{SakaéFuchino2004,
abstract = {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.},
author = {Sakaé Fuchino, Stefan Geschke},
journal = {Fundamenta Mathematicae},
keywords = {weak Freese-Nation property; SEP; Cohen model; almost disjoint number},
language = {eng},
number = {3},
pages = {233-255},
title = {Some combinatorial principles defined in terms of elementary submodels},
url = {http://eudml.org/doc/283366},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Sakaé Fuchino
AU - Stefan Geschke
TI - Some combinatorial principles defined in terms of elementary submodels
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 3
SP - 233
EP - 255
AB - 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.
LA - eng
KW - weak Freese-Nation property; SEP; Cohen model; almost disjoint number
UR - http://eudml.org/doc/283366
ER -