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The cofinality of the saturated uncountable random graph

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Abstract.

Assuming CH, let be the saturated random graph of cardinality ω1. In this paper we prove that it is consistent that and can be any two prescribed regular cardinals subject only to the requirement

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References

  1. Baumgartner, J.: Iterated Forcing. In: Surveys in Set Theory, A.R.D. Mathias, (ed.), Cambridge University Press, 1983, pp. 1–59

  2. Evans, D.: Examples of ω-categorical structures. In: Automorphisms of First Order Structures, R. Kaye and D. Macpherson, (eds.), Oxford, University Press Oxford, 1994, pp. 33–72

  3. Hodges, W., Hodkinson, I., Lascar, D., Shelah, S.: The Small Index Property for ω-Stable ω-Categorical Structures and for the Random Graph. J. London Math. Soc. (2) 48, 204–218 (1993)

    Google Scholar 

  4. Lascar, D.: On the Category of Models of a Complete Theory. J. Symbolic Logic 47, 249–266 (1982)

    MathSciNet  MATH  Google Scholar 

  5. Lascar, D., Shelah, S.: Uncountable Saturated Structures Have the Small Index Property. Bull. London Math. Soc. 25, 125–131 (1993)

    MathSciNet  MATH  Google Scholar 

  6. Macpherson, H.D., Neumann, P.M.: Subgroups of Infinite Symmetric Groups. J. London Math. Soc. (2) 42, 64–84 (1990)

    Google Scholar 

  7. Mildenberger, H., Shelah, S.: The Relative Consistency of Preprint 2000

  8. Sharp, J.D., Thomas, S.: Uniformization Problems and the Cofinality of the Infinite Symmetric Group. Notre Dame J. Formal Logic 35, 328–245 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sharp, J.D., Thomas, S.: Unbounded Families and the Cofinality of the Infinite Symmetric Group. Arch. Math. Logic 34, 33–45 (1995)

    Article  MathSciNet  Google Scholar 

  10. Thomas, S.: The Cofinalities of the Infinite Dimensional Classical Groups. J. Algebra 179, 704–719 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Truss, J.K.: Generic Automorphisms of Homogeneous Structures. Proc. London Math. Soc. (3) 65, 121–141 (1992)

  12. Warner, S.: The Cofinality of the Random Graph. J. Symbolic Logic (3) 6, 1439–1446 (2001)

    Google Scholar 

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  1. Department of Mathematics, Hofstra University, USA

    Steve Warner

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  1. Steve Warner
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Correspondence to Steve Warner.

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Warner, S. The cofinality of the saturated uncountable random graph. Arch. Math. Logic 43, 665–679 (2004). https://doi.org/10.1007/s00153-004-0223-5

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