# Universal Horn Sentences and the Joint Embedding Property

arXiv: https://arxiv.org/abs/2104.11123 · HTML: https://mlsanity.com/paper/2104.11123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Directed Regular and Context-Free Languages](https://mlsanity.com/paper/2401.07106/) (2024)

## Abstract (arXiv)

The finite models of a universal sentence Phi in a finite relational signature are the age of a structure if and only if Phi has the joint embedding property. We prove that the computational problem whether a given universal sentence Phi has the joint embedding property is undecidable, even if Phi is additionally Horn and the signature of Phi only contains relation symbols of arity at most two.