On the number of automorphisms of uncountable models

Journal of Symbolic Logic 58 (4):1402-1418 (1993)
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Abstract

Let σ(U) denote the number of automorphisms of a model U of power ω1. We derive a necessary and sufficient condition in terms of trees for the existence of an U with $\omega_1 < \sigma(\mathfrak{U}) < 2^{\omega_1}$. We study the sufficiency of some conditions for σ(U) = 2ω1 . These conditions are analogous to conditions studied by D. Kueker in connection with countable models

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Jouko A Vaananen
University of Helsinki

Citations of this work

Closed Maximality Principles and Generalized Baire Spaces.Philipp Lücke - 2019 - Notre Dame Journal of Formal Logic 60 (2):253-282.
Games and trees in infinitary logic: A survey.Jouko Väänänen - 1995 - In Michał Krynicki, Marcin Mostowski & Lesław W. Szczerba (eds.), Quantifiers: Logics, Models and Computation: Volume Two: Contributions. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 105--138.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
An ideal game.F. Galvin, T. Jech & M. Magidor - 1978 - Journal of Symbolic Logic 43 (2):284-292.
Infinite games and reduced products.W. Hodges - 1981 - Annals of Mathematical Logic 20 (1):77.

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