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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.0106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-30T13:29:26Z","cross_cats_sorted":[],"title_canon_sha256":"437d90436c9f733f2ba0b48a1eaf5572e38fb6b21471afd163a87947a91060e0","abstract_canon_sha256":"a173816386014a33d2369a221dfdb4b5d0b02155d7736dcf13aa1f83009aadb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:32.109735Z","signature_b64":"jLlJs/EyPPlb5Qq/jsF3axT7ZTs/zDWAGvk3OWJ4Bq+YiQWKiamxcTcHR2C7A5untPLRE+IWaU/wDL2Xf7YGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6da53e818af716cd877f4e48483233604ebf8d09baa600eefee72c88ce8b5529","last_reissued_at":"2026-05-18T00:34:32.109305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:32.109305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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