The present paper addresses the problem of attainment of the supremums in various equivalent definitions of the hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the variants considered) this is the best result we can expect.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-9,
author = {Andrzej Ros\l anowski and Saharon Shelah},
title = {Forcing for hL and hd},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {273-310},
zbl = {0982.03028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-9}
}
Andrzej Rosłanowski; Saharon Shelah. Forcing for hL and hd. Colloquium Mathematicae, Tome 89 (2001) pp. 273-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-9/