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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-3-5,
author = {Michael Hru\v s\'ak},
title = {Another [?]-like principle},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {277-289},
zbl = {0972.03046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-3-5}
}
Michael Hrušák. Another ⋄-like principle. Fundamenta Mathematicae, Tome 167 (2001) pp. 277-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-3-5/