Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: He, Jialiang, Luo, Jintao, Zhang, Shuguo
Institution: Sichuan University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3120576102
OpenAlex ID: W4415964193
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