Sh:1123

• Shelah, S., & Verner, J. L. Ramsey partitions of metric spaces. Journal of Combinatorial Theory. Preprint.
• Abstract:
  We investigate the existence of metric spaces which, for any coloring with a fixed number of colors, contain monochromatic isomorphic copies of a fixed starting space K. In the main theorem we construct such a space of size 2^{\aleph_0} for colorings with \aleph_0 colors and any metric space K of size \aleph_0. We also give a slightly weaker theorem for countable ultrametric K where, however, the resulting space has size \aleph_1.
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@article{Sh:1123,
 author = {Shelah, Saharon and Verner, Jonathan L.},
 title = {{Ramsey partitions of metric spaces}},
 journal = {Journal of Combinatorial Theory}
}