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The cofinality of the random graph

Published online by Cambridge University Press:  12 March 2014

Steve Warner*
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08854-8019, USA, E-mail: swarner@math.rutgers.edu

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
Copyright
Copyright © Association for Symbolic Logic 2001

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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. 3372.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. 204218.CrossRefGoogle Scholar
[3]Hrushovski, E., Extending partial automorphisms, of graphs, Combinatorica, vol. 12 (1992), pp. 411416.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. 249266.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. 6484.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. 3345.CrossRefGoogle Scholar
[9]Thomas, S., The cofinalities of the infinite dimensional classical groups, Journal of Algebra, vol. 179 (1996), pp. 704719.CrossRefGoogle Scholar
[10]Truss, J. K., Generic automorphisms of homogeneous structures, Proceedings of the London Mathematical Society, vol. 65 (1992), no. 3, pp. 121141.CrossRefGoogle Scholar