### A saturated model of an unsuperstable theory of cardinality greater than its theory has the small index property

by Melles and Shelah. [MeSh:450]

Proc London Math Soc, 1994

A model M of cardinality lambda is said to have the small
index property if for every G subseteq Aut(M) such that
[Aut(M):G] <= lambda there is an A subseteq M with |A|<
lambda such that Aut_A(M) subseteq G . We show that if M^* is
a
saturated model of an unsuperstable theory of cardinality > Th(M),
then M^* has the small index property.

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