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Automorphism Groups of Generic Structures: Extreme Amenability and Amenability

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arxiv 1508.04628 v2 pith:S75WVACP submitted 2015-08-19 math.LO math.COmath.DSmath.GR

Zaniar Ghadernezhad , Hamed Khalilian , Massoud Pourmahdian This is my paper · ORCID
classification math.LOmath.COmath.DSmath.GR
keywords genericamenabilityautomorphismgroupsstructurese-hrushovskiobtainedamenable
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We investigate correspondences between extreme amenability and amenability of automorphism groups of Fra\"iss\'e-Hrushovski generic structures that are obtained from smooth classes, and their Ramsey type properties of their smooth classes, similar to Kechris, Pestov and Todorcevic, and Tatch Moore. In particular, we focus on some Fra\"iss\'e-Hrushovski generic structures that are obtained from pre-dimension functions. Using these correspondences, we prove that automorphism groups of ordered Hrushovski generic graphs are not extremely amenable in both cases of collapsed and uncollapsed. Moreover, we prove that automorphism groups of Fra\"iss\'e-Hrushovski generic structures that are obtained from pre-dimension functions with rational coefficients are not amenable.

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Cited by 2 Pith papers

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  1. Automorphisms of very general blow up

    math.AG 2026-08 conditional novelty 7.0 of 10

    For every projective variety of dimension at least two that is not a rational surface, blowing up sufficiently many very general points yields a variety with no nontrivial automorphism.

  2. Merges of Smooth Classes and Their Properties

    math.LO 2024-11 conditional novelty 6.0 of 10

    Merging two smooth structure classes can preserve the original generic limits, and with a parallel strongness condition every infinite existentially definable subset of the merge's first reduct is again the first gene...

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