Is there a Ramsey-Hindman theorem ?
Ethan Akin, Eli Glasner
TL;DR
This paper proves that a combined generalization of Ramsey and Hindman theorems does not exist, specifically showing that the property of containing a symmetric IP-set cannot be divided.
Contribution
It establishes the non-divisibility of the symmetric IP-set property, demonstrating a fundamental limitation in extending Ramsey-Hindman type theorems.
Findings
No joint generalization of Ramsey and Hindman theorems exists.
Symmetric IP-set property is not divisible.
The result clarifies limitations in combinatorial partition theorems.
Abstract
We show that there does not exist a joint generalization of the theorems of Ramsey and Hindman, or more explicitly, that the property of containing a symmetric IP-set is not divisible.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms