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arXiv · 2104.11123

Universal Horn Sentences and the Joint Embedding Property

Manuel Bodirsky·Jakub Rydval·André Schrottenloher
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Abstract

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.

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Manuel Bodirsky, Jakub Rydval, André Schrottenloher. 2021-04-22. Universal Horn Sentences and the Joint Embedding Property. https://doi.org/10.46298/dmtcs.7435

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