{"paper":{"title":"On Determinacy for Cut and Choose Games of Uncountable Length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maxwell Levine","submitted_at":"2026-07-03T15:56:26Z","abstract_excerpt":"We obtain results on cut and choose games for complete Boolean algebras. Zapletal proved that there is a Boolean algebra $\\mathbb{B}$ such that $\\mathcal{G}_\\omega^\\textsf{candc}(\\mathbb{B})$, the version of the game which ends on the $\\omega$'th round, is undetermined. We prove that, assuming the consistency of a proper class of supercompact cardinals, the limit version $\\mathcal{G}^{\\textsf{candc}}_{< \\lambda}(\\mathbb{B})$, in which there are $\\lambda$-many rounds but no concluding round, is consistently determined for all complete Boolean algebras $\\mathbb{B}$ and all successor cardinals $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03444","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}