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The Small Index Property for ω‐Stable ω‐Categorical Structures and for the Random Graph
Author(s) -
Hodges Wilfrid,
Hodkinson Ian,
Lascar Daniel,
Shelah Saharon
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.2.204
Subject(s) - countable set , automorphism , mathematics , categorical variable , property (philosophy) , combinatorics , automorphism group , discrete mathematics , index (typography) , graph , pure mathematics , statistics , computer science , philosophy , epistemology , world wide web
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.