{"paper":{"title":"The complexity of the reals in inner models of set theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Boban Velickovic, W. Hugh Woodin","submitted_at":"1995-01-02T00:00:00Z","abstract_excerpt":"The usual definition of the set of constructible reals is $\\Sigma ^1_2$. This set can have a simpler definition if, for example, it is countable or if every real is constructible.\n  H. Friedman asked if the set of constructible reals can be analytic or even Borel in a nontrivial way.  A related problem was posed by K. Prikry: can there exist a nonconstructible perfect set of constructible reals?  The main result of this paper is a negative answer to Friedman's question.  In fact we prove that if $M$ is an inner model of set theory and the set of reals in $M$ is analytic then either all reals a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9501203","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"}