The Ramsey property and higher dimensional mad families
Logic
2024-12-04 v3
Abstract
We prove that under a principle of Ramsey regularity there are no infinite maximal almost disjoint families with respect to the transfinitely iterated Fr\'echet 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.
Keywords
Cite
@article{arxiv.2003.10944,
title = {The Ramsey property and higher dimensional mad families},
author = {David Schrittesser and Asger Törnquist},
journal= {arXiv preprint arXiv:2003.10944},
year = {2024}
}
Comments
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