Geodesic
Universal Horn Sentences and the Joint Embedding Property
Discrete mathematics & theoretical computer science, special issue in honour of Maurice Pouzet, Tome 23 (2021-2022) no. 2.

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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.
DOI : 10.46298/dmtcs.7435
Classification : 03C13, 03D35, 08A70, 68Q25 
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     title = {Universal {Horn} {Sentences} and the {Joint} {Embedding} {Property}},
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Bodirsky, Manuel; Rydval, Jakub; Schrottenloher, André. Universal Horn Sentences and the Joint Embedding Property. Discrete mathematics & theoretical computer science, special issue in honour of Maurice Pouzet, Tome 23 (2021-2022) no. 2. doi : 10.46298/dmtcs.7435. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.7435/

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