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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Baumgartner, J.: Iterated Forcing. In: Surveys in Set Theory, A.R.D. Mathias, (ed.), Cambridge University Press, 1983, pp. 1–59
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
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)
Lascar, D.: On the Category of Models of a Complete Theory. J. Symbolic Logic 47, 249–266 (1982)
Lascar, D., Shelah, S.: Uncountable Saturated Structures Have the Small Index Property. Bull. London Math. Soc. 25, 125–131 (1993)
Macpherson, H.D., Neumann, P.M.: Subgroups of Infinite Symmetric Groups. J. London Math. Soc. (2) 42, 64–84 (1990)
Mildenberger, H., Shelah, S.: The Relative Consistency of Preprint 2000
Sharp, J.D., Thomas, S.: Uniformization Problems and the Cofinality of the Infinite Symmetric Group. Notre Dame J. Formal Logic 35, 328–245 (1994)
Sharp, J.D., Thomas, S.: Unbounded Families and the Cofinality of the Infinite Symmetric Group. Arch. Math. Logic 34, 33–45 (1995)
Thomas, S.: The Cofinalities of the Infinite Dimensional Classical Groups. J. Algebra 179, 704–719 (1996)
Truss, J.K.: Generic Automorphisms of Homogeneous Structures. Proc. London Math. Soc. (3) 65, 121–141 (1992)
Warner, S.: The Cofinality of the Random Graph. J. Symbolic Logic (3) 6, 1439–1446 (2001)
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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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DOI: https://doi.org/10.1007/s00153-004-0223-5