{"paper":{"title":"Chains of Baire class 1 functions and various notions of special trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.GN"],"primary_cat":"math.LO","authors_text":"Juris Stepr\\=ans, M\\'arton Elekes","submitted_at":"2011-09-24T16:19:15Z","abstract_excerpt":"Following Laczkovich we consider the partially ordered set $\\iB_1(\\RR)$ of Baire class 1 functions endowed with the pointwise order, and investigate the order types of the linearly ordered subsets. Answering a question of Komj\\'ath and Kunen we show (in $ZFC$) that special Aronszajn lines are embeddable into $\\iB_1(\\RR)$. We also show that under Martin's Axiom a linearly ordered set $\\mathbb{L}$ with $|\\mathbb{L}|<2^\\omega$ is embeddable into $\\iB_1(\\RR)$ iff $\\mathbb{L}$ does not contain a copy of $\\omega_1$ or $\\omega_1^*$. We present a $ZFC$-example of a linear order of size $2^\\omega$ show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5283","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"}