Sh:1123

• Shelah, S., & Verner, J. L. (2023). Ramsey partitions of metric spaces. Acta Math. Hungar., 169(2), 524–533. arXiv: 2210.12836 DOI: /10.1007/s10474-023-01318-6
• 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.
• Version 2023-03-05_3 (7p) published version (10p)

@article{Sh:1123,
 author = {Shelah, Saharon and Verner, Jonathan L.},
 title = {{Ramsey partitions of metric spaces}},
 journal = {Acta Math. Hungar.},
 volume = {169},
 number = {2},
 year = {2023},
 pages = {524--533},
 doi = {/10.1007/s10474-023-01318-6},
 note = {\href{https://arxiv.org/abs/2210.12836}{arXiv: 2210.12836}},
 arxiv_number = {2210.12836}
}