{"paper":{"title":"On effective sigma-boundedness and sigma-compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vladimir Kanovei","submitted_at":"2011-10-05T08:20:23Z","abstract_excerpt":"We prove several theorems on sigma-bounded and sigma-compact pointsets. We start with a known theorem by Kechris, saying that any lightface \\Sigma^1_1 set of the Baire space either is effectively sigma-bounded (that is, covered by a countable union of compact lightface \\Delta^1_1 sets), or contains a superperfect subset (and then the set is not sigma-bounded, of course). We add different generalizations of this result, in particular, 1) such that the boundedness property involved includes covering by compact sets and equivalence classes of a given finite collection of lightface \\Delta^1_1 equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0919","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"}