On sets with rank one in simple homogeneous structures
We study definable sets D of SU-rank 1 in , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...