{"paper":{"title":"A note on the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Toshimichi Usuba","submitted_at":"2019-03-31T02:10:05Z","abstract_excerpt":"We construct a normal countably tight $T_1$ space $X$ with $t(X_\\delta) >2^\\omega$. This is an answer to the question posed by Dow-Juh\\'asz-Soukup-Szentmikl\\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\\delta$-modifications of countably tight spaces can be arbitrary large up to the least $\\omega_1$-strongly compact cardinal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00322","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"}