Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Horn Sentences and the Joint Embedding Property   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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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex