On the number of automorphisms of uncountable models

by Shelah and Tuuri and Vaananen. [ShTV:377]
J Symbolic Logic, 1993
Let s(A) denote the number of automorphisms of a model A of power omega_1 . We derive a necessary and sufficient condition in terms of trees for the existence of an A with omega_1 < s(A) < 2^{omega_1} . We study the sufficiency of some conditions for s(A)=2^{omega_1} . These conditions are analogous to conditions studied by D.Kueker in connection with countable models.

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