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Infinite Permutation Groups of Rapid Growth
Author(s) -
Macpherson H. D.
Publication year - 1987
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/s2-35.2.276
Subject(s) - permutation (music) , categorical variable , independence (probability theory) , mathematics , property (philosophy) , domain (mathematical analysis) , instability , stability (learning theory) , combinatorics , permutation group , pure mathematics , physics , computer science , mathematical analysis , statistics , philosophy , epistemology , machine learning , acoustics , mechanics
If M is an ℵ 0 ‐categorical structure of domain M , then for all k ∈N the number n k (Aut M) of orbits of Aut M on k ‐subsets of M is finite. Connections are here investigated between different growth rates for n k (Aut M) and various model‐theoretic properties of M, such as ω‐stability, instability, and the independence property.