Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXVII, No. 28, pp. 93–106 (2003) 

Universal minimal flows of automorphism groupsA. S. Kechris, V. Pestov and S. TodorcevicDepartment of Mathematics, Caltech 25337, Pasadena, CA 91125, kechris@caltech.eduDepartment of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario, Canada K1N6N5, vpest283@science.ottawa.ca Institute of Mathematics, SANU, Knez Mihailova 15, 11000 Beograd, Yugoslavia, stevo@mi.sanu.ac.yu Abstract: We investigate some connections between the Fra\"{i}sse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. We show, in particular, that results from the structural Ramsey theory can be quite useful in recognizing the universal minimal flows of this kind of groups. As result we compute universal minimal flows of several well known topological groups such as, for example, the automorphism group of the random graph, the automorphism group of the random trianglefree graph, the automorphism group of the $\infty$dimensional vector space over a finite field, the automorphism group of the countable atomless Boolean algebra,etc. So we have here a reversal in the traditional relationship between topological dynamics and Ramsey theory, the Ramseytheoretic results are used in proving theorems of topological dynamics rather than vice versa. Keywords: group actions, universal minimal flows, Fra\"{i}sse theory, structural Ramsey theory Classification (MSC2000): 05D10, 05C55, 22A10, 22A05, 22F05, 37B05, 37F20, 54H20 Full text of the article: (for faster download, first choose a mirror)
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