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Ramsey expansions of S-metric spaces

  • Jan Hubička
  • Matěj Konečný
  • Jaroslav Nešetřil
  • Norbert Sauer
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Abstract

Let S⊆ ℝ+ be a subset of positive reals. We say that a metric space is an S-metric space if the range of the metric is a subset of S∪ {0}. In 2007, Delhommé, Laflamme, Pouzet, and Sauer characterized those sets S for which the class of all finite S-metric spaces has the amalgamation property. Given an amalgamation class, a natural question is what its Ramsey expansion is. Ramsey expansions are known for classes of S-metric spaces for which S∪{0} carries a natural distance monoid structure, for example for S=ℚ+ or when S is topologically closed. In this paper, we extend this result to all amalgamation classes of finite S-metric spaces, thereby completing the Ramsey-theoretic classification of amalgamation classes of finite S-metric spaces.

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Cite

BibTeXRIS
BibTeX
@misc{hubicka2026ramsey,
  title = {{Ramsey expansions of $S$-metric spaces}},
  author = {Jan Hubička and Matěj Konečný and Jaroslav Nešetřil and Norbert Sauer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26167},
  eprint = {2610.26167},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26167},
}
RIS
TY  - UNPB
TI  - Ramsey expansions of S-metric spaces
AU  - Jan Hubička
AU  - Matěj Konečný
AU  - Jaroslav Nešetřil
AU  - Norbert Sauer
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26167
UR  - https://arxiv.org/abs/2610.26167
AB  - Let S⊆ ℝ^+ be a subset of positive reals. We say that a metric space is an S-metric space if the range of the metric is a subset of S∪ {0}. In 2007, Delhommé, Laflamme, Pouzet, and Sauer characterized those sets S for which the class of all finite S-metric spaces has the amalgamation property. Given an amalgamation class, a natural question is what its Ramsey expansion is. Ramsey expansions are known for classes of S-metric spaces for which S∪{0} carries a natural distance monoid structure, for example for S=ℚ^+ or when S is topologically closed. In this paper, we extend this result to all amalgamation classes of finite S-metric spaces, thereby completing the Ramsey-theoretic classification of amalgamation classes of finite S-metric spaces.
ER  -