The finite models of a universal sentence $\Phi$ 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 is binary.

翻译：通用判决的有限模式$\Phi$是一个结构的时代,如果而且只有$\Phi$拥有共同嵌入的财产。 我们证明,一个特定通用判决$\Phi$是否拥有共同嵌入的财产的计算问题是无法确定的,即使$\Phi$是Horn额外的,签名是二进制。