In his paper in Fund. Math. 178 (2003), Miller presented two conjectures regarding MAD families. The first is that CH implies the existence of a MAD family that is also a σ-set. The second is that under CH, there is a MAD family concentrated on a countable subset. These are proved in the present paper.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-2,
author = {J\"org Brendle and Greg Piper},
title = {MAD families with strong combinatorial properties},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {7-21},
zbl = {1111.03045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-2}
}
Jörg Brendle; Greg Piper. MAD families with strong combinatorial properties. Fundamenta Mathematicae, Tome 193 (2007) pp. 7-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-2/