, Volume 30, Issue 2, pp 415–426 | Cite as

Automorphism Groups of Countably Categorical Linear Orders are Extremely Amenable

  • François Gilbert Dorais
  • Steven Gubkin
  • Daniel McDonald
  • Manuel Rivera


We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite ordered structures with finitely many partial equivalence relations with convex classes.


Linear orders Automorphism groups Countable categoricity Extreme amenability Fraïssé classes Ramsey property 

Mathematics Subject Classifications (2010)

Primary 06A05 20B27; Secondary 03C35 05C55 


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  1. 1.
    Fraïssé, R.: Sur l’extension aux relations de quelques propriétés des ordres. Ann. Sci. Ecole Norm. Sup. 71(3), 363–388 (1954)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Hodges, W.: A Shorter Model Theory. Cambridge University Press, Cambridge (1997)zbMATHGoogle Scholar
  3. 3.
    Kechris, A.S., Pestov, V.G., Todorcevic, S.: Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geom. Funct. Anal. 15(1), 106–189 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Nguyen Van Thé, L.: Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups. Eur. J. Comb. 30(4), 934–945 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Pestov, V.G.: On free actions, minimal flows, and a problem by Ellis. Trans. Am. Math. Soc. 350(10), 4149–4165 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Rado, R.: Direct decomposition of partitions. J. Lond. Math. Soc. 29, 71–83 (1954)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Ramsey, F.P.: On a problem of formal logic. Proc. Lond. Math. Soc. 30, 264–286 (1930)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Rosenstein, J.G.: \(\aleph \sb{0}\)-categoricity of linear orderings. Fund. Math. 64, 1–5 (1969)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Rosenstein, J.G.: Linear orderings. In: Pure and Applied Mathematics, vol. 98. Academic Press, New York (1982)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • François Gilbert Dorais
    • 1
  • Steven Gubkin
    • 2
  • Daniel McDonald
    • 3
  • Manuel Rivera
    • 4
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA
  3. 3.Department of MathematicsUniversity of IllinoisUrbanaUSA
  4. 4.MathematicsCUNY Graduate CenterNew YorkUSA

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