On the number of automorphisms of uncountable models

Saharon Shelah, Heikki Tuuri, Jouko Väänänen
1993 Journal of Symbolic Logic (JSL)  
Let σ() denote the number of automorphisms of a model of power ω 1. We derive a necessary and sufficient condition in terms of trees for the existence of an with . We study the sufficiency of some conditions for . These conditions are analogous to conditions studied by D. Kueker in connection with countable models.
doi:10.2307/2275150 fatcat:37n73ynqcrgqnevrllsomwdpgm