{"paper":{"title":"Four Games on Boolean Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Boris Sobot, Milos S. Kurilic","submitted_at":"2013-03-30T13:29:26Z","abstract_excerpt":"The games G_2 and G_3 are played on a complete Boolean algebra B in \\omega-many moves. At the beginning White picks a non-zero element p of B and, in the n-th move, White picks a positive p_n < p and Black chooses an i_n belonging to {0,1}. White wins G_2 iff liminf p_n^{i_n}=0 and wins G_3 iff \\bigvee_{A\\in [\\omega ]^\\omega}\\bigwedge_{n\\in A}p_n^{i_n}=0. It is shown that White has a winning strategy in the game G_2 iff White has a winning strategy in the cut-and-choose game G_c&c introduced by Jech. Also, White has a winning strategy in the game G_3 iff forcing by B produces a subset R of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0106","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"}