Binary simple homogeneous structures are supersimple with finite rank (Q2790281)

A homogeneous structure is a countable structure \(M\) in a relational language such that every isomorphism between finite substructures of \(M\) can be extended to an automorphism of \(M\). If the structure \(M\) is assumed to be stable, then it is in fact \(\omega\)-stable. The purpose of this article is to try to understand homogeneous structures that are simple (in the model-theoretic sense). There seem to be very few results in this direction. The main point of this article is to prove that, under the extra assumption that \(M\) is binary (meaning every symbol in the language is either unary or binary), then \(M\) is in fact supersimple and the \(\mathrm{SU}\)-rank of \(M\) is at most the size of the set of 2-types over the theory.