Another ⋄-like principle

Michael Hrušák. "Another ⋄-like principle." Fundamenta Mathematicae 167.3 (2001): 277-289. <http://eudml.org/doc/282180>.

@article{MichaelHrušák2001,
abstract = {A new ⋄-like principle $⋄_\{\}$ consistent with the negation of the Continuum Hypothesis is introduced and studied. It is shown that $¬ ⋄_\{\}$ is consistent with CH and that in many models of = ω₁ the principle $⋄_\{\}$ holds. As $⋄_\{\}$ implies that there is a MAD family of size ℵ₁ this provides a partial answer to a question of J. Roitman who asked whether = ω₁ implies = ω₁. It is proved that $⋄_\{\}$ holds in any model obtained by adding a single Laver real, answering a question of J. Brendle who asked whether = ω₁ in such models.},
author = {Michael Hrušák},
journal = {Fundamenta Mathematicae},
keywords = { principle;  principle; cardinal invariants of the continuum; dominating family; maximal almost disjoint family; Laver real; random real},
language = {eng},
number = {3},
pages = {277-289},
title = {Another ⋄-like principle},
url = {http://eudml.org/doc/282180},
volume = {167},
year = {2001},
}

TY - JOUR
AU - Michael Hrušák
TI - Another ⋄-like principle
JO - Fundamenta Mathematicae
PY - 2001
VL - 167
IS - 3
SP - 277
EP - 289
AB - A new ⋄-like principle $⋄_{}$ consistent with the negation of the Continuum Hypothesis is introduced and studied. It is shown that $¬ ⋄_{}$ is consistent with CH and that in many models of = ω₁ the principle $⋄_{}$ holds. As $⋄_{}$ implies that there is a MAD family of size ℵ₁ this provides a partial answer to a question of J. Roitman who asked whether = ω₁ implies = ω₁. It is proved that $⋄_{}$ holds in any model obtained by adding a single Laver real, answering a question of J. Brendle who asked whether = ω₁ in such models.
LA - eng
KW -  principle;  principle; cardinal invariants of the continuum; dominating family; maximal almost disjoint family; Laver real; random real
UR - http://eudml.org/doc/282180
ER -