{"docId":9423,"paperId":7435,"url":"https:\/\/dmtcs.episciences.org\/7435","doi":"10.46298\/dmtcs.7435","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":419,"name":"vol. 23 no. 2, special issue in honour of Maurice Pouzet"}],"section":[{"sid":109,"title":"Special issues","description":[]}],"repositoryName":"arXiv","repositoryIdentifier":"2104.11123","repositoryVersion":6,"repositoryLink":"https:\/\/arxiv.org\/abs\/2104.11123v6","dateSubmitted":"2021-05-02 16:39:49","dateAccepted":"2022-04-09 17:06:00","datePublished":"2022-05-06 14:58:29","titles":["Universal Horn Sentences and the Joint Embedding Property"],"authors":["Bodirsky, Manuel","Rydval, Jakub","Schrottenloher, Andr\u00e9"],"abstracts":["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.","Comment: 16 pages"],"keywords":["Computer Science - Logic in Computer Science","Mathematics - Logic"]}