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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