Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T08:32:37.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces

Published online by Cambridge University Press:  20 November 2018

L. Nguyen Van Thé
L. Nguyen Van Thé*
Affiliation:
Equipe de Logique Mathématique, UFR de Mathématiques, Université Denis Diderot Paris 7, 75251 Paris Cedex 05, France. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given a countable set $S$ of positive reals, we study finite-dimensional Ramsey-theoretic properties of the countable ultrametric Urysohn space ${{\text{Q}}_{S}}$ with distances in $S$.

Keywords

05C5054E35Ramsey theoryUrysohn metric spacesultrametric spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 413 - 423
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Delhommé, C., Laflamme, C., Pouzet, M., and Sauer, N., Divisibility of countable metric spaces. European J. Combin. 28(2007), no. 6, 1746–1769.Google Scholar
[2] Erdőos, P. and Hajnal, A., Unsolved problems in set theory. In: Axiomatic Set Theory. Proc. Sympos. Pure Math. 13, American Mathematical Society, Providence, RI, 1971, pp. 17–48.Google Scholar
[3] Haddad, L. and Sabbagh, G., Sur une extension des nombres de Ramsey aux ordinaux. C. R. Acad. Sci. Paris Sér. A-B 268(1969), A1165–A1167.Google Scholar
[4] Haddad, L. and Sabbagh, G., Calcul de certains nombres de Ramsey généralisés. C. R. Acad. Sci. Paris Sér. A-B 268(1969), A1233–A1234.Google Scholar
[5] Haddad, L. and Sabbagh, G., Nouveaux résultats sur les nombres de Ramsey généralisés. C. R. Acad. Sci. Paris Sér. A-B 268(1969), A1516–A-1518.Google Scholar
[6] Kechris, A. S., Pestov, V., and Todorcevic, S., Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geom. Funct. Anal. 15(2005), no. 1, 106–189.Google Scholar
[7] Milner, E. C., A finite algorithm for the partition calculus. In: Proceedings of the Twenty-Fifth Summer Meeting of the Canadian Mathematical Congress. Lakehead University, Thunder Bay, ON, 1971, pp. 117–128.Google Scholar
[8] Nguyen Van Thé, L., Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups. European J. Combin., to appear.Google Scholar
[9] Urysohn, P., Sur un espace métrique universel. Bull. Sci. Math. 51(1927). 43–64, 74–90.Google Scholar