# Sh:450

• Melles, G., & Shelah, S. (1994). A saturated model of an unsuperstable theory of cardinality greater than its theory has the small index property. Proc. London Math. Soc. (3), 69(3), 449–463.
• Abstract:
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]\leq\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.
• published version (15p)
Bib entry
@article{Sh:450,
author = {Melles, Garvin and Shelah, Saharon},
title = {{A saturated model of an unsuperstable theory of cardinality greater than its theory has the small index property}},
journal = {Proc. London Math. Soc. (3)},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
volume = {69},
number = {3},
year = {1994},
pages = {449--463},
issn = {0024-6115},
doi = {10.1112/plms/s3-69.3.449},
mrclass = {03C50 (03C45)},
mrnumber = {1289859},
mrreviewer = {G. Cherlin},
doi = {10.1112/plms/s3-69.3.449},
note = {\href{https://arxiv.org/abs/math/9308216}{arXiv: math/9308216}},
arxiv_number = {math/9308216}
}