Kechris, Alexander S. and Sokić, Miodrag (2012) Dynamical properties of the automorphism groups of the random poset and random distributive lattice. Fundamenta Mathematicae, 218 (1). pp. 69-94. ISSN 0016-2736 http://resolver.caltech.edu/CaltechAUTHORS:20121126-103335875
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A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property.
|Additional Information:||© 2012 Instytut Matematyczny PAN. Received 24 October 2011; in revised form 7 June 2012. The research of the rst author was partially supported by NSF Grant DMS-0968710.|
|Subject Keywords:||automorphism groups; amenability; random poset; random distributive lattice; universal minimal flow; Ramsey theory|
|Classification Code:||2010 Mathematics Subject Classification: Primary 03C15, 05D10; Secondary 43A07, 37B05|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||26 Nov 2012 19:44|
|Last Modified:||26 Nov 2012 19:44|
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