Séminaires : Séminaire de Logique Lyon-Paris

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Responsables :O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
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Orateur(s) David Evans - Imperial College London,
Titre Higher amalgamation in measurable structures
Date20/05/2019
Horaire15:10 à 16:10
Diffusion
RésumeMeasurable structures were introduced by Macpherson and Steinhorn in 2008. Their definition abstracts certain properties of pseudofinite fields (following work of Chatzidakis, van den Dries and Macintyre) and has as a consequence that MS-measurable structures are supersimple of finite rank.

We give a higher amalgamation property which holds in MS-measurable structures (and more general contexts) which is a straightforward consequence of an infinitary formulation due to Towsner of the Hypergraph Removal Lemma.

It is an open question whether omega-categorical MS-measurable structures are necessarily one-based. Hrushovski constructions could potentially give counterexamples, but it is not known whether these can be MS-measurable. However, as a consequence of the higher amalgamation result, we can at least give an example of an omega-categorical supersimple Hrushovski construction which is not MS-measurable.

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