{"paper":{"title":"Andrews' Type Theory with Undefinedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"William M. Farmer","submitted_at":"2014-06-29T11:44:19Z","abstract_excerpt":"${\\cal Q}_0$ is an elegant version of Church's type theory formulated and extensively studied by Peter B. Andrews. Like other traditional logics, ${\\cal Q}_0$ does not admit undefined terms. The \"traditional approach to undefinedness\" in mathematical practice is to treat undefined terms as legitimate, nondenoting terms that can be components of meaningful statements. ${\\cal Q}^{\\rm u}_{0}$ is a modification of Andrews' type theory ${\\cal Q}_0$ that directly formalizes the traditional approach to undefinedness. This paper presents ${\\cal Q}^{\\rm u}_{0}$ and proves that the proof system of ${\\ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7492","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"}