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Uncountable Saturated Structures have the Small Index Property

Uncountable Saturated Structures have the Small Index Property We prove the following theorem. Let m be an uncountable saturated structure of cardinality λ = λ<λ and assume that G is a subgroup of Aut (m) whose index is less than or equal to λ. Then there exists a subset A of cardinality strictly less than λ such that every automorphism of m leaving A pointwise fixed is in G. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Uncountable Saturated Structures have the Small Index Property

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/25.2.125
Publisher site
See Article on Publisher Site

Abstract

We prove the following theorem. Let m be an uncountable saturated structure of cardinality λ = λ<λ and assume that G is a subgroup of Aut (m) whose index is less than or equal to λ. Then there exists a subset A of cardinality strictly less than λ such that every automorphism of m leaving A pointwise fixed is in G.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Mar 1, 1993

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