{"paper":{"title":"Decidable fragments of the Simple Theory of Types with Infinity and NF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Anuj Dawar, Thomas Forster, Zachiri McKenzie","submitted_at":"2014-06-17T14:34:35Z","abstract_excerpt":"We identify complete fragments of the Simple Theory of Types with Infinity ($\\mathrm{TSTI}$) and Quine's $\\mathrm{NF}$ set theory. We show that $\\mathrm{TSTI}$ decides every sentence $\\phi$ in the language of type theory that is in one of the following forms:\n  (A) $\\phi= \\forall x_1^{r_1} \\cdots \\forall x_k^{r_k} \\exists y_1^{s_1} \\cdots \\exists y_l^{s_l} \\theta$ where the superscripts denote the types of the variables, $s_1 > \\ldots > s_l$ and $\\theta$ is quantifier-free,\n  (B) $\\phi= \\forall x_1^{r_1} \\cdots \\forall x_k^{r_k} \\exists y_1^{s} \\cdots \\exists y_l^{s} \\theta$ where the superscr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4384","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"}