Topological Ramsey numbers and countable ordinals

  title={Topological Ramsey numbers and countable ordinals},
  author={Andr{\'e}s Eduardo Caicedo and Jacob Hilton},
  journal={arXiv: Logic},
We study the topological version of the partition calculus in the setting of countable ordinals. Let α and β be ordinals and let k be a positive integer. We write β →top (α, k)² to mean that, for every red-blue coloring of the collection of 2-sized subsets of β, there is either a red-homogeneous set homeomorphic to α or a blue-homogeneous set of size k. The least such β is the topological Ramsey number Rtop(α, k). We prove a topological version of the Erdős-Milner theorem, namely that Rtop(α, k… 

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