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.

URL:https://www.imj-prg.fr/spip.php?article189 END:VEVENT END:VCALENDAR