{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:22Z","timestamp":1753889842292,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T00:00:00Z","timestamp":1372118400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We investigate tree-automatic well-founded trees. Using Delhomme's\ndecomposition technique for tree-automatic structures, we show that the\n(ordinal) rank of a tree-automatic well-founded tree is strictly below\nomega^omega. Moreover, we make a step towards proving that the ranks of\ntree-automatic well-founded partial orders are bounded by omega^omega^omega: we\nprove this bound for what we call upwards linear partial orders. As an\napplication of our result, we show that the isomorphism problem for\ntree-automatic well-founded trees is complete for level Delta^0_{omega^omega}\nof the hyperarithmetical hierarchy with respect to Turing-reductions.<\/jats:p>","DOI":"10.2168\/lmcs-9(2:10)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:39:25Z","timestamp":1385732365000},"source":"Crossref","is-referenced-by-count":0,"title":["Tree-Automatic Well-Founded Trees"],"prefix":"10.46298","volume":"Volume 9, Issue 2","author":[{"given":"Martin","family":"Huschenbett","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Kartzow","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0824-0899","authenticated-orcid":false,"given":"Jiamou","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"Lohrey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,6,25]]},"reference":[{"key":"806:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/721\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/721\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:54:37Z","timestamp":1681242877000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,25]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(2:10)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1201.5495","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1201.5495","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2013,6,25]]},"article-number":"721"}}