{"paper":{"title":"Frechet Borel Ideals with Borel orthogonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Carlos Uzcategui, Francisco Guevara","submitted_at":"2013-12-15T00:37:17Z","abstract_excerpt":"We study Borel ideals $I$ on $\\mathbb{N}$ with the Fr\\'echet property such its orthogonal $I^\\perp$ is also Borel (where $A\\in I^\\perp$ iff $A\\cap B$ is finite for all $B\\in I$ and $I$ is Fr\\'echet if $I=I^{\\perp\\perp}$). Let $\\mathcal{B}$ be the smallest collection of ideals on ${\\mathbb{N}}$ containing the ideal of finite sets and closed under countable direct sums and orthogonal. All ideals in $\\mathcal{B}$ are Fr\\'echet, Borel and have Borel orthogonal. We show that $\\mathcal{B}$ has exactly $\\aleph_1$ non isomorphic members. The family $\\mathcal{B}$ can be characterized as the collection "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4095","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"}