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arXiv · 2504.12746

A note on one-variable theorems for NSOP

Will Johnson
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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.

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Will Johnson. 2025-04-17. A note on one-variable theorems for NSOP. https://arxiv.org/abs/2504.12746

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