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arXiv · 2210.12836

Ramsey partitions of metric spaces

Saharon Shelah·Jonathan L. Verner
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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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Saharon Shelah, Jonathan L. Verner. 2022-10-23. Ramsey partitions of metric spaces. https://arxiv.org/abs/2210.12836

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