Using an infinitary version of the hypergraph removal lemma due to
Towsner, we prove a model-theoretic higher amalgamation result. In
particular, we obtain an independent amalgamation property which holds in
structures that are measurable in the sense of Macpherson and Steinhorn,
but which is not generally true in structures that are supersimple of finite
-rank.
We use this to show that some of Hrushovski’s non-locally-modular, supersimple
-categorical
structures are not MS-measurable.
Keywords
model theory, amalgamation properties, measurability,
pseudofiniteness, Hrushovski constructions