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arXiv · 2510.17399

Ramsey regularity implies no MAD families without uniformization

Jialiang He·Jintao Luo·Shuguo Zhang
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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.

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Jialiang He, Jintao Luo, Shuguo Zhang. 2025-10-20. Ramsey regularity implies no MAD families without uniformization. https://arxiv.org/abs/2510.17399

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