Journal of Symbolic Logic

On the Number of Automorphisms of Uncountable Models

Saharon Shelah, Heikki Tuuri, and Jouko Vaananen

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

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J. Symbolic Logic, Volume 58, Issue 4 (1993), 1402-1418.

First available in Project Euclid: 6 July 2007

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Shelah, Saharon; Tuuri, Heikki; Vaananen, Jouko. On the Number of Automorphisms of Uncountable Models. J. Symbolic Logic 58 (1993), no. 4, 1402--1418.

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