2017/11/06 by Omid Etesami, Etesami, Omid, Zaniar Ghadernezhad +1
Mathematics · #03C15 #05D10 #20B27 #43A07 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1711.02049
openalex publication_date 2017/11/06 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this paper we prove that the automorphism groups of certain countable\ngeneric structures are not amenable. For doing that, we first prove the\nexistence of particular matrices that do not satisfy the convex Ramsey\ncondition. For a pair of elements in a smooth class, we introduce the property\nof forming a free-pseudoplane in the generic structure. We then prove the\nnon-amenability of the automorphism group of a generic structure obtained from\na smooth class with a pair that forms a free-pseudoplane. As an application we\nshow that the automorphism group of an ab-initio generic structure that is\nconstructed using a pre-dimension function with irrational coefficients is not\namenable.\n