|Responsables :||S. Anscombe, A. Khélif, A. Vignati|
|Email des responsables :||firstname.lastname@example.org, email@example.com|
|Adresse :||Sophie Germain|
|Orateur(s)||David Evans - Imperial College London,|
|Titre||Higher amalgamation in measurable structures|
|Horaire||15:10 à 16:10|
|Résume||Measurable 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.