{"paper":{"title":"On ordinal ranks of Baire class functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"Denny H. Leung, Hong-Wai Ng, Wee-Kee Tang","submitted_at":"2017-01-20T00:47:56Z","abstract_excerpt":"The theory of ordinal ranks on Baire class 1 functions developed by Kechris and Loveau was recently extended by Elekes, Kiss and Vidny\\'{a}nszky to Baire class $\\xi$ functions for any countable ordinal $\\xi\\geq1$. In this paper, we answer two of the questions raised by them in their paper (Ranks on the Baire class $\\xi$ functions, Trans. Amer. Math. Soc. 368(2016), 8111-8143). Specifically, we show that for any countable ordinal $\\xi\\geq1,$ the ranks $\\beta_{\\xi}^{\\ast}$ and $\\gamma_{\\xi}^{\\ast}$ are essentially equivalent, and that neither of them is essentially multiplicative. Since the rank"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05649","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"}