Ramsey regularity implies no MAD families without uniformization
Logic
2025-10-21 v1
Abstract
We show that if the Ramsey property holds (in a class of sets), then there is no MAD family (in this class, provided it satisfies some modest closure properties), proving a conjecture made by A.R.D.\ Mathias in 1977. As the technique we introduce for this proof is useful in a variety of related problems, we take the opportunity to announce 4 theorems, which will be proved in a follow-up paper.
Cite
@article{arxiv.2510.17399,
title = {Ramsey regularity implies no MAD families without uniformization},
author = {Jialiang He and Jintao Luo and Shuguo Zhang},
journal= {arXiv preprint arXiv:2510.17399},
year = {2025}
}
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4 Pages