{"paper":{"title":"Complexity and (un)decidability of fragments of $\\langle \\omega^{\\omega^\\lambda}; \\times \\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Alexis B\\`es, Christian Choffrut","submitted_at":"2018-03-04T20:54:25Z","abstract_excerpt":"We specify the frontier of decidability for fragments of the first-order theory of ordinal multiplication. We give a NEXPTIME lower bound for the complexity of the existential fragment of $\\langle \\omega^{\\omega^\\lambda}; \\times, \\omega, \\omega+1, \\omega^2+1 \\rangle$ for every ordinal $\\lambda$. Moreover, we prove (by reduction from Hilbert Tenth Problem) that the $\\exists^*\\forall^{6}$-fragment of $\\langle \\omega^{\\omega^\\lambda}; \\times \\rangle$ is undecidable for every ordinal $\\lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01418","kind":"arxiv","version":2},"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"}