We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.
@article{bwmeta1.element.bwnjournal-article-fmv163i1p55bwm, author = {M. Losada and Stevo Todor\v cevi\'c}, title = {Chains and antichains in Boolean algebras}, journal = {Fundamenta Mathematicae}, volume = {163}, year = {2000}, pages = {55-76}, zbl = {0948.06010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p55bwm} }
Losada, M.; Todorčević, Stevo. Chains and antichains in Boolean algebras. Fundamenta Mathematicae, Tome 163 (2000) pp. 55-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p55bwm/
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