{"paper":{"title":"Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Samuele Maschio, Thomas Streicher","submitted_at":"2014-07-08T22:33:24Z","abstract_excerpt":"With every pca $\\mathcal{A}$ and subpca $\\mathcal{A}_\\#$ we associate the nested realizability topos $\\mathsf{RT}(\\mathcal{A},\\mathcal{A}_\\#)$ within which we identify a class of small maps $\\mathcal{S}$ giving rise to a model of intuitionistic set theory within $\\mathsf{RT}(\\mathcal{A},\\mathcal{A}_\\#)$. For every subtopos $\\mathcal{E}$ of such a nested realizability topos we construct an induced class $\\mathcal{S_E}$ of small maps in $\\mathcal{E}$ giving rise to a model of intuitionistic set theory within $\\mathcal{E}$. This covers relative realizability toposes, modified relative realizabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2287","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"}