Generalized amalgamation and homogeneity

preprint2016arXivOpen access

Abstract

In this paper we shall prove that any 22-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary homogeneous structures to arbitrary ones without binary relations. Furthermore, we point out a relation between generalized amalgamation, triviality and quantifier elimination in simple theories.

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