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Dual Ramsey Theorem for Trees

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Abstract

The classical Ramsey theorem was generalized in two major ways: to the dual Ramsey theorem, by Graham and Rothschild, and to Ramsey theorems for trees, initially by Deuber and Leeb. Bringing these two lines of thought together, we prove the dual Ramsey theorem for trees. Galois connections between partial orders are used in formulating this theorem, while the abstract approach to Ramsey theory, we developed earlier, is used in its proof.

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Acknowledgements

I would like to thank Miodrag Sokić and Anush Tserunyan for their remarks. I am also grateful to a referee for a careful reading of the paper and for suggestions that improved its presentation. Research supported by NSF Grants DMS-1266189, 1800680, and 1954069.

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  1. Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY, 14853, USA

    Sławomir Solecki

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Solecki, S. Dual Ramsey Theorem for Trees. Combinatorica 43, 91–128 (2023). https://doi.org/10.1007/s00493-023-00009-8

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