{"paper":{"title":"Characterization of order types of pointwise linearly ordered families of Baire class 1 functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"M\\'arton Elekes, Zolt\\'an Vidny\\'anszky","submitted_at":"2014-10-30T13:14:02Z","abstract_excerpt":"In the 1970s M. Laczkovich posed the following problem: Let $\\mathcal{B}_1(X)$ denote the set of Baire class $1$ functions defined on an uncountable Polish space $X$ equipped with the pointwise ordering. \\[\\text{Characterize the order types of the linearly ordered subsets of $\\mathcal{B}_1(X)$.} \\]The main result of the present paper is a complete solution to this problem.\n  We prove that a linear order is isomorphic to a linearly ordered family of Baire class $1$ functions iff it is isomorphic to a subset of the following linear order that we call $([0,1]^{<\\omega_1}_{\\searrow 0},<_{altlex})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8362","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"}