A saturated model of an unsuperstable theory of cardinality greater than its theory has the small index property. Melles, G. & Shelah, S. Proceedings of the London Mathematical Society, 69:449–463, 1994. arxiv:math/9308216
bibtex   
@article{MeSh:450,
author = {Melles, Garvin and Shelah, Saharon},
fromwhere = {1,IL},
journal = {Proceedings of the London Mathematical Society},
note = { arxiv:math/9308216 },
pages = {449--463},
title = {{A saturated model of an unsuperstable theory of cardinality
 greater than its theory has the small index property}},
volume = {69},
year = {1994},
}

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