Universal Horn Sentences and the Joint Embedding Property

04/22/2021

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by   Manuel Bodirsky, et al.

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The finite models of a universal sentence Φ are the age of a structure if and only if Φ has the joint embedding property. We prove that the computational problem whether a given universal sentence Φ has the joint embedding property is undecidable, even if Φ is additionally Horn and the signature is binary.