Submission date: 18 July 2018

Abstract:

We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets, or equivalently at most exponential growth of the number of finite substructures. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely many linear orders interacting in a restricted number of ways. As an example of application, we deduce the classification of primitive structures homogeneous in a language consisting of n linear orders as well as all reducts of such structures.

Mathematics Subject Classification: 03C15, 03C64, 03C68, 06A05

Keywords and phrases:

Full text arXiv 1807.07102: pdf, ps.