Linear orders in NIP structures

DOI10.1016/J.AIM.2021.108069arXiv1807.07949MaRDI QIDQ6304459

Publication date: 20 July 2018

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.

Mathematics Subject Classification ID

Mathematical logic and foundations (03-XX) Model theory (03Cxx) Ordered structures (06Fxx)

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