{"paper":{"title":"Randomness via infinite computation and effective descriptive set theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl, Philipp Schlicht","submitted_at":"2016-12-09T11:44:01Z","abstract_excerpt":"We study randomness beyond $\\Pi^1_1$-randomness and its Martin-L\\\"of type variant, introduced in \\cite{MR2340241} and further studied in \\cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\\ITTM s), introduced by Hamkins and Kidder, is strictly between $\\Pi^1_1$ and $\\Sigma^1_2$. We prove that the natural randomness notions associated to this class have several desirable properties resembling those of the classical random notions such as Martin-L\\\"of randomness, and randomness notions defined via effective descriptive set theory such as $\\Pi^1_1$-randomne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02982","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"}