{"paper":{"title":"The $ \\mathbf{\\Sigma}^1_2$ counterparts to statements that are equivalent to the Continuum Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asger Tornquist, William Weiss","submitted_at":"2012-01-01T20:24:08Z","abstract_excerpt":"We consider natural $\\Sigma^1_2$ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these $\\Sigma^1_2$ analogues are equivalent to that all reals are constructible. We also prove two partition relations for $\\Sigma^1_2$ colourings which hold precisely when there is a non-constructible real."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0382","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"}