Submission date: 12 August 2022

Abstract:

We study ω-categorical MS-measurable structures. Our main result is that a class of ω-categorical Hrushovski constructions, supersimple of finite SU-rank is not MS-measurable. These results complement the work of Evans on a conjecture of Macpherson and Elwes. Differently from Evans' work, our structures may satisfy independent n-amalgamation for all n. We also prove some general results in the context of ω-categorical MS-measurable structures. Firstly, in these structures the dimension in the MS-dimension-measure can be chosen to be SU-rank. Secondly, non-forking independence implies a form of probabilistic independence in the measure. The latter follows from more general unpublished results of Hrushovski, but we provide a self-contained proof.

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Full text arXiv 2208.06323: pdf, ps.