Ramsey partitions of metric spaces

by Shelah and Verner. [ShVr:1123]

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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