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arXiv · 2503.18727

Colors of the Pseudotree

David Chodounský·Monroe Eskew·Thilo Weinert
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Abstract

We investigate big Ramsey degrees of finite substructures of the universal countable homogeneous meet-tree and its binary variant. We prove that structures containing antichains have infinite big Ramsey degrees, and the big Ramsey degree of a 2-element chain is at least 8 and 7 for the binary variant. We deduce that the generic C-relation does not have finite big Ramsey degrees.

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David Chodounský, Monroe Eskew, Thilo Weinert. 2025-05-29. Colors of the Pseudotree. https://arxiv.org/abs/2503.18727

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