{"paper":{"title":"Mycielski among trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Marcin Michalski, Robert Ra{\\l}owski, Szymon \\.Zeberski","submitted_at":"2019-05-22T11:07:59Z","abstract_excerpt":"Two-dimensional version of the classical Mycielski theorem says that for every comeager or conull set $X\\subseteq [0,1]^2$ there exists a perfect set $P\\subseteq [0,1]$ such that $P\\times P\\subseteq X\\cup \\Delta$. We consider generalizations of this theorem by replacing a perfect square with a rectangle $A\\times B$, where $A$ and $B$ are bodies of other types of trees with $A\\subseteq B$. In particular, we show that for every comeager $G_\\delta$ set $G\\subseteq \\omega^\\omega\\times \\omega^\\omega$ there exist a Miller tree $M$ and a uniformly perfect tree $P\\subseteq M$ such that $[P]\\times [M]\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09069","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"}