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ℵ 0 ‐Categorical Structures Smoothly Approximated by Finite Substructures
Author(s) -
Kantor W. M.,
Liebeck Martin W.,
Macpherson H. D.
Publication year - 1989
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-59.3.439
Subject(s) - categorical variable , mathematics , simple (philosophy) , homogeneous , class (philosophy) , representation (politics) , pure mathematics , classification of finite simple groups , algebra over a field , combinatorics , group theory , artificial intelligence , computer science , statistics , group of lie type , philosophy , epistemology , politics , political science , law
A classification is given of primitive ℵ 0 ‐categorical structures which are smoothly approximated by a chain of finite homogeneous substructures. The proof uses the classification of finite simple groups and some representation theory. The main theorems give information about a class of structures more general than the ℵ 0 ‐categorical, ω‐stable structures examined by Cherlin, Harrington, and Lachlan.