We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-5,
author = {Andrzej Ros\l anowski and Saharon Shelah},
title = {Around cofin},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {211-225},
zbl = {1338.03094},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-5}
}
Andrzej Rosłanowski; Saharon Shelah. Around cofin. Colloquium Mathematicae, Tome 135 (2014) pp. 211-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-5/