## Journal of Symbolic Logic

### On the Number of Automorphisms of Uncountable Models

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744382

Mathematical Reviews number (MathSciNet)
MR1253929

Zentralblatt MATH identifier
0805.03019

JSTOR

#### Citation

Shelah, Saharon; Tuuri, Heikki; Vaananen, Jouko. On the Number of Automorphisms of Uncountable Models. J. Symbolic Logic 58 (1993), no. 4, 1402--1418. https://projecteuclid.org/euclid.jsl/1183744382