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

Research output: Contribution to journalArticlepeer-review

105 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 languageEnglish
Pages (from-to)204-218
Number of pages15
JournalJournal of the London Mathematical Society
Volumes2-48
Issue number2
DOIs
StatePublished - Oct 1993

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