Ramsey partitions of metric spaces

S. Shelah*, J. Verner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 2ℵ0 for colorings with ℵ colors and any metric space K of size ℵ. We also give a slightly weaker theorem for countable ultrametric K where, however, the resulting space has size ℵ1.

Original languageEnglish
Pages (from-to)524-533
Number of pages10
JournalActa Mathematica Hungarica
Volume169
Issue number2
DOIs
StatePublished - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023, Akadémiai Kiadó, Budapest, Hungary.

Keywords

  • arrow
  • metric space
  • Ramsey

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