{"paper":{"title":"Countable dense homogeneity and $\\lambda$-sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jan van Mill, Michael Hru\\v{s}\\'ak, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2018-09-18T16:33:22Z","abstract_excerpt":"We show that all sufficiently nice $\\lambda$-sets are countable dense homogeneous ($\\mathsf{CDH}$). From this fact we conclude that for every uncountable cardinal $\\kappa \\le \\mathfrak{b}$ there is a countable dense homogeneous metric space of size $\\kappa$. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size $\\kappa$ is equivalent to the existence of a $\\lambda$-set of size $\\kappa$. On the other hand, it is consistent with the continuum arbitrarily large that every $\\mathsf{CDH}$ metric space has size either $\\omega_1$ or size $\\mathfrak c$. An exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06819","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"}