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A collection of topological Ramsey spaces of trees and their application to profinite graph theory

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Abstract

We construct a collection of new topological Ramsey spaces of trees. It is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. We give an example of its application by proving a partition theorem for profinite graphs.

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Acknowledgements

I am grateful to Professor Stevo Todorcevic for his guidance. I would like to thank Osvaldo Guzmán González who pointed out a mistake in an earlier version of this work. I must also thank the Referee for pointing out another mistake.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Room 6290, 40 St. George Street, M5S 2E4, Toronto, ON, Canada

    Yuan Yuan Zheng

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  1. Yuan Yuan Zheng
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Correspondence to Yuan Yuan Zheng.

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This work was partially supported by the Queen Elizabeth II Graduate Scholarship in Science and Technology.

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Zheng, Y.Y. A collection of topological Ramsey spaces of trees and their application to profinite graph theory. Arch. Math. Logic 57, 939–952 (2018). https://doi.org/10.1007/s00153-018-0617-4

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  • DOI: https://doi.org/10.1007/s00153-018-0617-4

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