NIP omega-categorical structures: the rank 1 case
Logic
2022-08-02 v5 Combinatorics
Abstract
We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets. 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.
Cite
@article{arxiv.1807.07102,
title = {NIP omega-categorical structures: the rank 1 case},
author = {Pierre Simon},
journal= {arXiv preprint arXiv:1807.07102},
year = {2022}
}
Comments
Final version, accepted for publication in the Proceedings of the London Mathematical Society