The Ramsey property and higher dimensional mad families
arXiv:2003.10944
Abstract
We prove that under a principle of Ramsey regularity there are no infinite maximal almost disjoint families with respect to the transfinitely iterated Fréchet ideals. The results of the present paper were announced by the authors in the Proceedings of the National Academy of Sciences of the U.S.A.
30 pages. Several previously glossed over proof steps in Section 4 have been made explicit, making the proof easier to follow. The material contained in Section 5 of the previous version will appear separately