### 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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