A note on one-variable theorems for NSOP

Will Johnson

A note on one-variable theorems for NSOP

Logic 2025-07-15 v4

Authors: Will Johnson

Abstract

We give an example of an SOP theory $T$ , such that any $L(M)$ -formula $\varphi(x,y)$ with $|y|=1$ is NSOP. We show that any such $T$ must have the independence property. We also give a simplified proof of Lachlan's theorem that if every $L$ -formula $\varphi(x,y)$ with $|x|=1$ is NSOP, then $T$ is NSOP.

Cite

@article{arxiv.2504.12746,
  title  = {A note on one-variable theorems for NSOP},
  author = {Will Johnson},
  journal= {arXiv preprint arXiv:2504.12746},
  year   = {2025}
}