The Small Index Property for ω-Stable (ω-Categorical Structures and for the Random Graph

Wilfrid Hodges; Ian Hodkinson; Daniel Lascar; Saharon Shelah

doi:10.1112/jlms/s2-48.2.204

The Small Index Property for ω-Stable (ω-Categorical Structures and for the Random Graph

Wilfrid Hodges^*
, Ian Hodkinson
, Daniel Lascar
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

Abstract

We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any ω-stable ω-categorical structure, and (ii) the random graph have the small index property. We also show that the automorphism group of such a structure is not the union of a countable chain of proper subgroups.

Original language	English
Pages (from-to)	204-218
Number of pages	15
Journal	Journal of the London Mathematical Society
Volume	s2-48
Issue number	2
DOIs	https://doi.org/10.1112/jlms/s2-48.2.204
State	Published - Oct 1993

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The Small Index Property for ω-Stable (ω-Categorical Structures and for the Random Graph

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