A note on one-variable theorems for NSOP
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913939577634816 |
|---|---|
| author | Johnson, Will |
| author_facet | Johnson, Will |
| contents | We give an example of an SOP theory $T$, such that any $L(M)$-formula $φ(x,y)$ 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 $φ(x,y)$ with $|x|=1$ is NSOP, then $T$ is NSOP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on one-variable theorems for NSOP Johnson, Will Logic 03C45 We give an example of an SOP theory $T$, such that any $L(M)$-formula $φ(x,y)$ 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 $φ(x,y)$ with $|x|=1$ is NSOP, then $T$ is NSOP. |
| title | A note on one-variable theorems for NSOP |
| topic | Logic 03C45 |
| url | https://arxiv.org/abs/2504.12746 |