{"paper":{"title":"Shooting a club with finite conditions","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jind\\v{r}ich Zapletal","submitted_at":"1994-03-10T00:00:00Z","abstract_excerpt":"We study cohabitation of the poset $P_S$ shooting a club through a given stationary subset $S$ of $\\omega _1$ with finite conditions with other forcings. Sample results:\n (1) $P_S$ \"sometimes\" preserves presaturatedness of $NS_{\\omega _1}$\n (2) $P_S=P_T$ if $S=T mod NS_{\\omega _1}$ (in Boolean algebra sense)\n (3) Cons ( one can embed $Q,$ the poset adding $\\aleph _1$ Cohen reals, to $P_S$ such that reals in $V^Q$ are the same as reals in $V^{P_S}.$ )"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9403202","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"}