{"paper":{"title":"More on the cut and choose game","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 improve some ancient results of Velickovic on the cut and choose (c&c) game on complete Boolean algebras.\n (1) If Nonempty has a winning strategy for c&c game on $B$ then $B$ is semiproper.\n (2) If Nonempty has a winning strategy and $B$ has $2^{\\aleph _0}$ -c.c. then Nonempty has a winning strategy in the descending chain game.\n (3) Cons ($B$ is $\\aleph _1$-distributive implies Nonempty has a winning strategy in c&c on $B$ )\n  We also give some new examples of forcings where Nonempty has or does not have a winning strategy in c&c game."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9403203","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"}