On the Number of Automorphisms of Uncountable Models
Shelah, Saharon ; Tuuri, Heikki ; Vaananen, Jouko
J. Symbolic Logic, Tome 58 (1993) no. 1, p. 1402-1418 / Harvested from Project Euclid
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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.
Publié le : 1993-12-14
Classification:  
@article{1183744382,
     author = {Shelah, Saharon and Tuuri, Heikki and Vaananen, Jouko},
     title = {On the Number of Automorphisms of Uncountable Models},
     journal = {J. Symbolic Logic},
     volume = {58},
     number = {1},
     year = {1993},
     pages = { 1402-1418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744382}
}

Shelah, Saharon; Tuuri, Heikki; Vaananen, Jouko. On the Number of Automorphisms of Uncountable Models. J. Symbolic Logic, Tome 58 (1993) no. 1, pp.  1402-1418. http://gdmltest.u-ga.fr/item/1183744382/