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- W4300919905 abstract "In this paper we prove that the automorphism groups of certain countable generic structures are not amenable. For doing that, we first prove the existence of particular matrices that do not satisfy the convex Ramsey condition. For a pair of elements in a smooth class, we introduce the property of forming a free-pseudoplane in the generic structure. We then prove the non-amenability of the automorphism group of a generic structure obtained from a smooth class with a pair that forms a free-pseudoplane. As an application we show that the automorphism group of an ab-initio generic structure that is constructed using a pre-dimension function with irrational coefficients is not amenable." @default.
- W4300919905 created "2022-10-04" @default.
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- W4300919905 date "2017-11-06" @default.
- W4300919905 modified "2023-09-28" @default.
- W4300919905 title "Convex Ramsey matrices and non-amenability of automophism groups of generic structures" @default.
- W4300919905 doi "https://doi.org/10.48550/arxiv.1711.02049" @default.
- W4300919905 hasPublicationYear "2017" @default.
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