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More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

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Asymptotic Geometric Analysis

Part of the book series: Fields Institute Communications ((FIC,volume 68))

Abstract

In this paper, we compute universal minimal flows of groups of automorphisms of uncountable ω-homogeneous graphs, K n -free graphs, hypergraphs, partially ordered sets, and their extensions with an ω-homogeneous ordering. We present an easy construction of such structures, expanding the jungle of extremely amenable groups.

Mathematical Subject Classifications (2010): 37B05, 03E02, 05D10, 22F50, 54H20

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References

  1. D. Bartošová, Universal minimal flows of groups of automorphisms of uncountable structures. In Canadian Mathematical Bulletin, Published electronically on July 27 (2012). http://dx.doi.org:10.4153/CMB-2012-023-4

    Google Scholar 

  2. J. de Vries, Elements of topological dynamics. In Mathematics and its Applications, vol. 257 (Kluwer, Dordrecht, 1993)

    Google Scholar 

  3. R. Fraïssé, Sur l’extension aux relations de quelques propriétés des ordres. Ann. Sci. Ecole Norm. Sup. 71(3), 363–388 (1954)

    MathSciNet  MATH  Google Scholar 

  4. W. Herer, J.P.R. Christensen, On the existence of pathological submeasures and the construction of exotic topological groups. Math. Ann. 213 203–210 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Hodges, A Shorter Model Theory (Cambridge University Press, Cambridge, 1997)

    MATH  Google Scholar 

  6. B. Jónsson, Universal relational systems. Math. Scand. 4, 193–208 (1956)

    MathSciNet  MATH  Google Scholar 

  7. B. Jónsson, Homogeneous universal relational systems. Math. Scand. 8, 137–142 (1960)

    MathSciNet  MATH  Google Scholar 

  8. A.S. Kechris, V.G. Pestov, S. Todorčević. Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geom. Funct. Anal. 15(1), 106–189 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Nešetřil, V. Rödl, Partitions of finite relational and set systems. J. Combinatorial Theory Ser. A 22(3), 289–312 (1977)

    MathSciNet  MATH  Google Scholar 

  10. J. Nešetřil, V. Rödl, On a probabilistic graph-theoretical method. Proc. Amer. Math. Soc. 72(2), 417–421 (1978)

    MathSciNet  MATH  Google Scholar 

  11. J. Nešetřil, V. Rödl, Ramsey classes of set systems. J. Combin. Theory Ser. A 34(2), 183–201 (1983)

    Article  MathSciNet  Google Scholar 

  12. V.G. Pestov, On free actions, minimal flows, and a problem by Ellis. Trans. Amer. Math. Soc. 350(10), 4149–4165 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Shelah, On universal graphs without instances of CH. Ann. Pure Appl. Logic 26(1), 75–87 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Sokic, Ramsey property of posets and related structures. Ph.D. Thesis, 2010

    Google Scholar 

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Acknowledgements

This project was partially supported by the grant GAUK 66509. I wish to thank Stevo Todorčević for proposing the project of computing universal minimal flows of groups of automorphisms of uncountable structures, for introducing me to Jónsson structures and suggesting the present construction of ω-homogeneous structures. I am also grateful to Lionel Nguyen Van Thé and the anonymous referee for careful reading and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 2E4

    Dana Bartošová

  2. Charles University in Prague, Ke Karlovu 3, 121 16, Prague, Czech Republic

    Dana Bartošová

Authors
  1. Dana Bartošová
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Correspondence to Dana Bartošová .

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Editors and Affiliations

  1. TU Wien, Wiedner Hauptstrasse 8–10, Wien, 1040, Austria

    Monika Ludwig

  2. Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Schreiber Building 334, Tel Aviv, 69978, Israel

    Vitali D. Milman

  3. University of Ottawa, Ottawa, K1N 6N5, Canada

    Vladimir Pestov

  4. , Department of Math and Stat Scis, University of Alberta, Central Academic Bldg 632, Edmonton, T6G 2G1, Alberta, Canada

    Nicole Tomczak-Jaegermann

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Bartošová, D. (2013). More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_2

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