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Colors of the Pseudotree

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arxiv 2503.18727 v2 pith:HZW5ZENC submitted 2025-03-24 math.CO math.LO

David Chodounský , Monroe Eskew , Thilo Weinert This is my paper · ORCID
classification math.COmath.LO
keywords ramseydegreesbinaryfinitevariantantichainsc-relationchain
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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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  1. Oscillating subalgebras of the atomless countable Boolean algebra

    math.LO 2025-05 conditional novelty 7.0 of 10

    The big Ramsey degree of the 3-atom Boolean algebra in the countable atomless Boolean algebra is infinite.

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