{"paper":{"title":"Intersection properties of open sets, II.","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"I. Juh\\'asz, Lajos Soukup, Zs. Nagy, Z. Szentmikl\\'ossy","submitted_at":"1996-05-06T00:00:00Z","abstract_excerpt":"A topological space is called P_2 ( P_3, P_{<omega} ) if and only if it does not contain two (three, finitely many) uncountable open sets with empty intersection.\n  We show that\n (i)   there are  0-dimensional P_{<omega} spaces  of size 2^omega,\n (ii)  there are compact P_{<omega} spaces of size omega_1,\n (iii) the existence of a Psi-like examples for a compact P_{<omega} space of size omega_1  is independent of ZFC,\n (iv)  it is consistent that 2^omega  is as large as you wish but every first countable (and so every compact) P_2 space has cardinality<=omega_1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9605209","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"}