Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-06T18:01:03.535Z Has data issue: false hasContentIssue false
  • English
  • Français

The cofinality of the random graph

Published online by Cambridge University Press:  12 March 2014

Steve Warner
Steve Warner*
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08854-8019, USA, E-mail: swarner@math.rutgers.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that under Martin's Axiom, the cofinality cf(Aut(Γ)) of the automorphism group of the random graph Γ is 2ω.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1439 - 1446
Copyright
Copyright © Association for Symbolic Logic 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Evans, D., Examples of ω-categorical structures, Automorphisms offirst order structures (Kaye, R. and Macpherson, D., editors), Oxford University Press, Oxford, 1994, pp. 33–72.CrossRefGoogle Scholar
[2]Hodges, W., Hodkinson, I., Lascar, D., and Shelah, S., The small index property for ω-stable ω-categorical structures and for the random graph, Journal of the London Mathematical Society, vol. 48 (1993), no, 2, pp. 204–218.CrossRefGoogle Scholar
[3]Hrushovski, E., Extending partial automorphisms, of graphs, Combinatorica, vol. 12 (1992), pp. 411–416.CrossRefGoogle Scholar
[4]Kechris, A. S., Classical descriptive set theory, Springer-Verlag, New York, 1995.CrossRefGoogle Scholar
[5]Lascar, D., On the category of models of a complete theory, this Journal, vol. 47 (1982), pp. 249–266.Google Scholar
[6]Macpherson, H. D. and Neumann, P. M., Subgroups of infinite symmetric groups, Journal of the London Mathematical Society, vol. 42 (1990), no. 2, pp. 64–84.CrossRefGoogle Scholar
[7]Sharp, J. D. and Thomas, S., Uniformization problems and the cofinality of the infinite symmetric group, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 328–245.CrossRefGoogle Scholar
[8]Sharp, J. D. and Thomas, S., Unbounded families and the cofinality of the infinite symmetric group, Archive of Mathematical Logic, vol. 34 (1995), pp. 33–45.CrossRefGoogle Scholar
[9]Thomas, S., The cofinalities of the infinite dimensional classical groups, Journal of Algebra, vol. 179 (1996), pp. 704–719.CrossRefGoogle Scholar
[10]Truss, J. K., Generic automorphisms of homogeneous structures, Proceedings of the London Mathematical Society, vol. 65 (1992), no. 3, pp. 121–141.CrossRefGoogle Scholar