{"paper":{"title":"Projective maximal families of orthogonal measures with large continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asger Tornquist, Sy-David Friedman, Vera Fischer","submitted_at":"2011-06-21T17:24:15Z","abstract_excerpt":"We study maximal orthogonal families of Borel probability measures on $2^\\omega$ (abbreviated m.o. families) and show that there are generic extensions of the constructible universe $L$ in which each of the following holds:\n  (1) There is a $\\Delta^1_3$-definable well order of the reals, there is a $\\Pi^1_2$-definable m.o. family, there are no $\\mathbf{\\Sigma}^1_2$-definable m.o. families and $\\mathfrak{b}=\\mathfrak{c}=\\omega_3$ (in fact any reasonable value of $\\mathfrak{c}$ will do).\n  (2) There is a $\\Delta^1_3$-definable well order of the reals, there is a $\\Pi^1_2$-definable m.o. family, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4273","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"}