{"paper":{"title":"Countable dense homogeneity in powers of zero-dimensional definable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Andrea Medini","submitted_at":"2014-08-09T17:04:52Z","abstract_excerpt":"We show that, for a coanalytic subspace $X$ of $2^\\omega$, the countable dense homogeneity of $X^\\omega$ is equivalent to $X$ being Polish. This strengthens a result of Hru\\v{s}\\'ak and Zamora Avil\\'es. Then, inspired by results of Hern\\'andez-Guti\\'errez, Hru\\v{s}\\'ak and van Mill, using a technique of Medvedev, we construct a non-Polish subspace $X$ of $2^\\omega$ such that $X^\\omega$ is countable dense homogeneous. This gives the first $\\mathsf{ZFC}$ answer to a question of Hru\\v{s}\\'ak and Zamora Avil\\'es. Furthermore, since our example is consistently analytic, the equivalence result menti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2137","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"}