Advertisement

Archive for Mathematical Logic

, Volume 50, Issue 1–2, pp 215–221 | Cite as

The conjugacy problem for the automorphism group of the random graph

Article

Abstract

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

Keywords

Borel equivalence relations Random graph Categorical structure 

Mathematics Subject Classification (2000)

03E15 03C15 05C80 08A35 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Becker H., Kechris A.S.: The descriptive set theory of Polish group actions, volume 232 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1996)Google Scholar
  2. 2.
    Camerlo R., Gao S.: The completeness of the isomorphism relation for countable Boolean algebras. Trans. Am. Math. Soc. 353(2), 491–518 (2001) (electronic)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Foreman, M.: A descriptive view of ergodic theory. In: Descriptive set theory and dynamical systems (Marseille-Luminy, 1996), volume 277 of London Mathematical Society Lecture Note Series, pp. 87–171. Cambridge University Press, Cambridge (2000)Google Scholar
  4. 4.
    Friedman H., Stanley L.: A Borel reducibility theory for classes of countable structures. J. Symb. Logic 54(3), 894–914 (1989)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Glass, A.M.W.: Ordered permutation groups, volume 55 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1981)Google Scholar
  6. 6.
    Hjorth G., Kechris A.S.: Borel equivalence relations and classifications of countable models. Ann. Pure Appl. Logic 82(3), 221–272 (1996)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Macpherson D., Woodrow R.: The permutation group induced on a moiety. Forum Math. 4(3), 243–255 (1992)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Truss J.K.: The group of the countable universal graph. Math. Proc. Cambridge Philos. Soc. 98(2), 213–245 (1985)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Truss J.K.: The automorphism group of the random graph: four conjugates good, three conjugates better. Discrete Math 268(1–3), 257–271 (2003)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe Graduate Center of the City University of New YorkNew YorkUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA
  3. 3.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA

Personalised recommendations