{"paper":{"title":"Automatic Ordinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"IMJ), Olivier Finkel (ELM, Stevo Todorcevic (ELM","submitted_at":"2012-05-08T19:05:08Z","abstract_excerpt":"We prove that the injectively omega-tree-automatic ordinals are the ordinals smaller than $\\omega^{\\omega^\\omega}$. Then we show that the injectively $\\omega^n$-automatic ordinals, where $n>0$ is an integer, are the ordinals smaller than $\\omega^{\\omega^n}$. This strengthens a recent result of Schlicht and Stephan who considered in [Schlicht-Stephan11] the subclasses of finite word $\\omega^n$-automatic ordinals. As a by-product we obtain that the hierarchy of injectively $\\omega^n$-automatic structures, n>0, which was considered in [Finkel-Todorcevic12], is strict."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1775","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}