Dynamical properties of the automorphism groups of the random poset and random distributive lattice
Tom 218 / 2012
Fundamenta Mathematicae 218 (2012), 69-94
MSC: Primary 03C15, 05D10; Secondary 43A07, 37B05.
DOI: 10.4064/fm218-1-4
Streszczenie
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.
