Linear orders in NIP structures
Logic
2021-07-02 v3
Abstract
We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a longstanding open question.
Cite
@article{arxiv.1807.07949,
title = {Linear orders in NIP structures},
author = {Pierre Simon},
journal= {arXiv preprint arXiv:1807.07949},
year = {2021}
}
Comments
21 pages. Many clarifications and corrections were made made following a referee report. Proofs are more detailed