{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T01:39:33Z","timestamp":1779154773039,"version":"3.51.4"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2007,1,25]],"date-time":"2007-01-25T00:00:00Z","timestamp":1169683200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/assumed-1991-2003"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A relational structure is a core, if all its endomorphisms are embeddings.\nThis notion is important for computational complexity classification of\nconstraint satisfaction problems. It is a fundamental fact that every finite\nstructure has a core, i.e., has an endomorphism such that the structure induced\nby its image is a core; moreover, the core is unique up to isomorphism. Weprove\nthat every \\omega -categorical structure has a core. Moreover, every\n\\omega-categorical structure is homomorphically equivalent to a model-complete\ncore, which is unique up to isomorphism, and which is finite or \\omega\n-categorical. We discuss consequences for constraint satisfaction with \\omega\n-categorical templates.<\/jats:p>","DOI":"10.2168\/lmcs-3(1:2)2007","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T11:44:52Z","timestamp":1212493492000},"source":"Crossref","is-referenced-by-count":37,"title":["Cores of Countably Categorical Structures"],"prefix":"10.46298","volume":"Volume 3, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8228-3611","authenticated-orcid":false,"given":"Manuel","family":"Bodirsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2007,1,25]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/2224\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/2224\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:09:55Z","timestamp":1681243795000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/2224"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,25]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-3(1:2)2007","relation":{"is-same-as":[{"id-type":"arxiv","id":"cs\/0612069","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.cs\/0612069","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1602.04353","asserted-by":"subject"},{"id-type":"doi","id":"10.1145\/2933575.2934544","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1602.04353","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1,25]]},"article-number":"2224"}}